Strategic Conformity in Affiliate Marketing

Strategic Conformity in Aﬃliate Marketing

Itay Fainmesser

∗

Xudong Zheng

†

February 29, 2024

Abstract

Aﬃliate marketing is a prevalent performance-based marketing model. For the most part,

retailers have formally transitioned from paying marketing aﬃliates pay-per-click to a pay-

per-purchase compensation model. Yet, some pay-per-click incentives remain in many aﬃliate

programs. Our results show that the remaining pay-per-click incentives give rise to a conﬂict

of interest between aﬃliates and consumers. On the one hand, consumer surplus is maximized

under aﬃliates’ recommendation conformity, i.e., when aﬃliates converge on a single product

in their recommendation proﬁle. On the other hand, if aﬃliates are compensated signiﬁcantly

per click, they achieve the highest aggregate payoﬀs by minimizing recommendation confor-

mity. Surprisingly, even if aﬃliates are compensated mostly per purchase and both consumers

and aﬃliates would beneﬁt from recommendation conformity, a conformity equilibrium may not

exist. In contrast, a non-conformity equilibrium always exists. We characterize further how con-

sumers’ expected search length, aﬃliates’ product information accuracy, and consumers’ ability

to learn directly about products’ qualities aﬀect market outcomes via its eﬀect on the existence

of conformity equilibria. Finally, our results shed light on how a retailer can craft aﬃliates’

compensation structure to inﬂuence market outcomes.

Keywords: Aﬃliate marketing, Strategic conformity

∗

The Johns Hopkins Carey Business School and The Department of Economics, The Johns Hopkins University,

Baltimore, MD 21202 (e-mail: itay fainmesser@jhu.edu)

†

The Department of Economics, The Johns Hopkins University, Baltimore, MD 21218 (e-mail: [email protected])

1 Introduction

Aﬃliates are websites (e.g., Wirecutter, CNET), bloggers, and social media inﬂuencers, who pro-

mote a retailer’s product or service (Shopify 2024) using unique aﬃliate links—links that allow

tracking by the retailer. An aﬃliate directs a consumer to a product’s web page on the retailer’s

online platform, and is compensated based on the consumer’s action. Common compensation

models include pay-per-click (the retailer pays the aﬃliate for each click on an aﬃliate link by a

consumer) and pay-per-purchase (the retailer pays the aﬃliate for each purchase by a consumer

who is directed to the platform by the aﬃliate’s link). Aﬃliate marketing is becoming increasingly

important to consumers and retailers. Since its inception in the mid-90s, aﬃliate marketing has

experienced a 10% year-on-year growth, becoming an industry worth over 15.7 billion U.S. dollars

in 2023,

accounting for 16% of all internet orders globally (a staggering 53% of all sales on Amazon

came from aﬃliates).

As a result, it is not surprising that over 80 percent of retailers consider

aﬃliate marketing to be a key way to promote products and engage consumers (Jeﬀerson 2016).

Yet despite the prominence of aﬃliate marketing in practice, scant research has focused on aﬃliates’

strategic product recommendations.

This paper develops a new model that captures three key features of aﬃliate marketing: (1) the

majority of pay-per-purchase aﬃliate programs use a “cookie duration” to provide aﬃliates with

pay-per-click-like incentives,

(2) consumers often contribute more clicks than purchases during

their search processes, and (3) consumers and aﬃliates may be more likely to be aware of some

prominent products ex ante (e.g., a running shoe from Nike) than of other less prominent products

(e.g., a running shoe from Hoka)—we refer to such prominent product as salient products, and to

aﬃliates’ tendency to converge in their recommendations and recommend the same salient product

Source: Printify, https://printify.com/blog/affiliate-marketing-trends/, accessed January 25,

2024.

Source: Demandsage, https://www.demandsage.com/affiliate-marketing-statistics/, accessed

January 25, 2024.

That is, once a consumer clicks on an aﬃliate link, a cookie is set, and the aﬃliate receives a commission for the

consumer’s ﬁrst purchase on website within a speciﬁc time frame, typically from twenty-four hours to several months.

Notably, the aﬃliate receives a commission even if the consumer buys a diﬀerent product than the one recommended.

as recommendation conformity.

4,5

We answer the following questions:

1. How is recommendation conformity related to other market outcomes, such as aﬃliates’ ag-

gregate proﬁts and consumer surplus?

2. How does the aﬃliate program’s commission structure, in particular pay-per-purchase vs. pay-

per-click, aﬀect aﬃliates’ recommendation conformity, and subsequently the related market

outcomes?

3. Does increasing the information that aﬃliates have on products’ qualities (e.g., by allowing

aﬃliates to test products) make aﬃliates’ recommendation conformity more or less likely?

4. How do features of consumers’ search, such as search duration and the ability to observe a

product’s quality, aﬀect aﬃliates’ recommendation conformity?

Our analysis shows that two aﬃliates’ recommendation proﬁles are especially important when

it comes to welfare outcomes. In a non-conformity strategy proﬁle, aﬃliates disregard the salient

product, and each recommends a non-salient product for which he received a high quality signal.

On the other extreme, in a conformity strategy proﬁle, every aﬃliate who receives a high quality

signal for the salient product, recommends the salient product. A non-conformity equilibrium and

a conformity equilibrium are equilibria in which aﬃliates employ non-conformity and conformity

strategy proﬁles respectively.

Our ﬁrst result shows that a conformity strategy proﬁle always maximizes the (expected) Con-

sumer Surplus (CS). If aﬃliates’ compensation has a signiﬁcant per-purchase component, then a

conformity strategy proﬁle also maximizes aﬃliates’ aggregate expected payoﬀ, or Aﬃliate Sur-

Our notion of conformity is distinct from the one studied in the (sequential) social learning literature on online

reviews (Moe and Trusov 2011, Moe and Schweidel 2012, Sridhar and Srinivasan 2012). In that literature reviewers

may observe earlier reviews and, through belief updating, have their opinions (and reviews) align with existing

reviews. In contrast, aﬃliates in our framework provide their recommendations simultaneously. That is, their

recommendation conformity is a strategic outcome based on aﬃliates’ focus on maximizing their expected earnings

given their compensation structure.

In our model, there are many ex-ante substitutable products, each of either high or low quality. One of the

products is “salient” in the following sense: Each aﬃliate observes signals that contains information on the quality of

the salient product and the qualities of a randomly selected sample of the non-salient products. That is, all aﬃliates

receive signals on the quality of the salient product, and it is highly unlikely that any two aﬃliates receive signals

on the quality of the same non-salient product. As a result, recommendation conformity on a non-salient product is

ruled-out.

plus (AS).

In that case, consumers and aﬃliates have aligned preferences for conformity. How-

ever, if aﬃliates’ compensation has a signiﬁcant per-click component, then AS is maximized by

a non-conformity strategy proﬁle.

In that case, consumers’ and aﬃliates’ preferences for payoﬀ

maximization are polar opposites. That is, we provide a bang-bang result: either AS and CS are

maximized by the same recommendation strategy proﬁle or by opposing ones.

To see why a conformity strategy proﬁle always maximizes CS, note that a conformity strat-

egy proﬁle aggregates the most accurate information about the quality of the salient product. If

the salient product receives many recommendations, it is very likely to be of high quality. The

consumer’s belief induces her to inspect it ﬁrst and likely to make a purchase, thus ending her

costly search after one click. The relationship between conformity and AS is more subtle. On

the one hand, when aﬃliates are compensated heavily per purchase, they want to convert the

consumer’s clicks to purchases eﬀectively, so that the consumer purchases with high probability

before stopping to search. On the other hand, when aﬃliates are compensated heavily per click,

they seek to maximize clicks, hence, they might prefer to risk the consumer stopping the search

without purchasing, if that means the consumer clicks on more links in expectations. The aﬃliates’

compensation threshold for preferring conformity over non-conformity depends on the consumer’s

expected search duration (in case of no purchase) and the accuracy of aﬃliates’ information on

product quality: (a) the shorter the expected search the better oﬀ aﬃliates are in focusing on a

conformity strategy proﬁle that maximizes the probability of purchase, and (b) the more accurate

the aﬃliates’ information, the more certain they are that the search will end with a purchase, so

their focus shifts to maximizing clicks.

Our second and third results show that a non-conformity equilibrium always exists, whereas

the existence of a conformity equilibrium subtly depends on aﬃliates’ compensation. In fact, even

when both the consumer and the aﬃliates would beneﬁt from aﬃliates’ conformity, a conformity

equilibrium may not exist, leading to a sub-optimal welfare outcome. Yet, when aﬃliates’ payoﬀs

are maximized with a non-conformity strategy proﬁle, a conformity equilibrium can exist. This

suggests that conﬂict of interest built into the market structure may make it challenging for aﬃliates

to coordinate on an equilibrium that is good for them and they may, instead, end with a market

The same is true if the consumer is likely to abort the search quickly in the absence of a purchase, or if aﬃliates’

information about products’ qualities is likely inaccurate.

The same is true if the consumer is likely to continue searching for longer, or if aﬃliates’ information about

products’ qualities is suﬃciently accurate.

outcome that is sub-optimal for them.

To see why a non-conformity equilibrium always exists, suppose that all but one aﬃliate recom-

mend non-salient products. In that case, the remaining aﬃliate will have no incentive to recommend

the salient product (regardless of his information about the salient product’s quality). The reason

is that salience leads the consumer to make quality inferences about the salient product based on

the absence of recommendations—if some aﬃliates do not recommend it, they might have learned

that the salient product has low quality. To the contrary, a conformity equilibrium may not exists

if either the incentives for aﬃliates to conform are two weak (for example if compensation is heavily

per click), or if their incentives to conform are too strong (for example if compensation is heavily

per purchase). In the case in which incentives to conform are too strong, if all other aﬃliates

employ conformity strategies, an aﬃliate would chose to recommend the salient product even if

he received a low quality signal for it—leading to the collapse of the equilibrium and unraveling

towards the non-conformity equilibrium.

An interesting implication of our results is that the retailer can aﬀect when a conformity equi-

librium exists through its control of aﬃliates’ compensation, changing the weight between per-click

and per-purchase compensation. However, the eﬀect of shifting compensation weights between

per-purchase and per-click is not straightforward and depends on the consumer’s expected search

duration in the following way: If a consumer is likely to abandon the search early, her ﬁrst click-

through is more critical to aﬃliates than the prospect of subsequent clicks. Hence, when aﬃliates

are paid per-click, a conformity equilibrium exists for a larger set of parameters. In contrast, when

the consumer’s expected search is longer, aﬃliates are less sensitive to the ﬁrst click. As a re-

sult, if consumer search is expected to be longer, a heavier pay-per-click component implies that a

conformity equilibrium exists for a smaller set of parameters.

We generalize our model to accommodate an environment in which the consumer cannot per-

fectly observe the true quality of a product after clicking on an aﬃliate link, but instead she observes

a noisy signal. We show that our results extend to this more general environment. The more gen-

eral model also allows us to derive additional comparative statics. Interestingly, in the limit case of

experience goods, where consumers do not observe any independent quality signal before purchase,

aﬃliates as a group become indiﬀerent between conformity and non-conformity strategy proﬁles,

and a conformity equilibrium exists for a smaller range of parameters.

Our paper continues as follows. We discuss our contribution to the literature in the remaining

of Section 1. Section 2 presents our baseline model. In Section 3, we present our results highlighting

the conﬂict of interest between aﬃliates and consumers, and characterize the existence of conformity

equilibria. Section 4 presents an extension generalizing the assumption on the consumer’s learning

and discusses implications for platform design. All proofs are deferred to the appendix.

1.1 Related Literature

Our paper contributes to the literature on social inﬂuencers. Katona (2020) analyzes how ﬁrms

compete for inﬂuencers considering the overlap and degrees in the inﬂuencers’ reach in a social

network. Fainmesser and Galeotti (2021) study a market in which inﬂuencers maximize sponsorship

revenues by choosing how much sponsored and organic content to post. Jain and Qian (2021)

analyze how competition among online content producers, the size of the consumer base, and

consumers’ time constraints aﬀect retailers’ revenue-sharing strategies. Pei and Mayzlin (2022)

study the optimal business relationship between a ﬁrm and inﬂuencers. Janssen and Williams

(2021) study the role of inﬂuencers in aﬀecting the order of consumer search. Berman et al. (2023)

investigate how social inﬂuencers’ creative contribution to a ﬁrm’s marketing campaign aﬀects

the ﬁrm’s proﬁt by inﬂuencing the dispersion of the market demand for its product. Nistor and

Selove (2022) focus on how an inﬂuencer’s entertainment level aﬀects the informativeness of their

comment section and which products they endorse. This literature focuses on inﬂuencers who are

paid per content endorsement (akin to how most advertisers are paid). Our main departure from

this literature is that we study a performance-based marketing model, aﬃliate marketing, in which

inﬂuencers are paid per performance (per click and/or per purchase).

There exists some empirical literature on aﬃliate marketing.

Papatla and Bhatnagar (2002)

demonstrates the eﬀect and advantage for an online retailer from having aﬃliates, even if such

aﬃliates are also retailers of related products. Olbrich et al. (2019) ﬁnd how Search Engine Opti-

mization (SEO) can cannibalize the eﬀect of aﬃliate marketing when merchants run multi-channel

campaigns. Additional work focuses on various practical issues related to aﬃliate marketing, such

as control mechanisms and contract designs (Gilliland and Rudd 2013), aﬃliate fraud (Edelman

Early case studies include Hoﬀman and Novak (2000) on one of the earliest and most successful aﬃliate program,

the BuyWeb Network of CD Now, a music retailer, and how it integrated aﬃliate marketing into its multifaceted cus-

tomer acquisition strategy, and Duﬀy (2005), identifying a key to successful aﬃliate marketing, i.e., the construction

of a win-win relationship between the advertiser and the aﬃliate.

and Brandi 2015), absence of endorsement disclosure (Mathur et al. 2018), deceptive and fabricated

reviews (Karabas et al. 2021), and eﬀects of language features on consumer engagement (Syrdal

et al. 2023).

To our knowledge, there are two papers studying aﬃliate marketing theoretically. Libai et al.

(2003) consider non-strategic aﬃliates and compares pay-per-purchase and pay-per-click from a

retailer’s perspective. Suryanarayana et al. (2019) study a model in which aﬃliates arrive sequen-

tially, and analyze a retailer’s optimal information disclosure to aﬃliates as they arrive. In this

paper there is only one product and the retailer maximizes the revenue from selling that product.

2 Model

Consider a market with many products, one of which is more salient than the others. Aﬃliates

(he/they) receive stochastic signals on the qualities of the products and each aﬃliate chooses

one product to recommend online by providing an aﬃliate link. A consumer (she) observes the

recommendations of the aﬃliates and decides whether to click on aﬃliate links as part of her costly

search for a high quality product. We next describe each of the components of our model: products,

the aﬃliates’ information sets, the consumer, and the timeline of the model.

2.1 Products

A single retailer (e.g., Amazon) simultaneously oﬀers a unit measure of distinct and substitutable

products online. Ex-ante, products are divided into two types. There is one commonly known

salient product, hereafter product 0.

The remaining products are non-salient. The formal diﬀer-

ence between the salient and non-salient products will become clear in Subsection 2.2. We denote

the set of non-salient products by NS.

Products are vertically diﬀerentiated. Each product i ∈ {0} ∪ NS, regardless of its salience,

has ex ante equal probability of being high or low quality, denoted by q

∈ {H, L}. That is,

P r(q

= H) = P r(q

= L) = 1/2. The realizations of products’ qualities are drawn independently.

The prices of the products are all equal and normalized to 1.

We leave unmodeled the reasons leading to product 0 being salient, such as brand market share, past marketing

campaigns, or superior brand awareness.

2.2 Aﬃliates’ Information

There are N aﬃliates, who actively post recommendations for the retailer’s products (each on his

channel, e.g., TikTok, YouTube, or a blog).

An aﬃliate j does not observe the qualities of the

products but receives a signal s

(i) ∈ {h, l} for each product i from a set η

⊂ {0}∪NS that includes

the salient product (product 0) and a countably inﬁnite collection of products chosen uniformly at

random (u.a.r.) from the set of non-salient products, N S.

The signal s

(i) is generated such that

P r(s

(i) = h|q

= H) = P r(s

(i) = l|q

= L) = p

> 1/2 for all j = 1, . . . , N and i ∈ η

. Signals

are conditionally independent across aﬃliates and products. Taking into account his signals, each

aﬃliate j recommends a single product online by posting an aﬃliate link. Such an aﬃliate link

can direct the consumer to the web page of the recommended product on the retailer’s online

marketplace.

Each aﬃliate maximizes his monetary compensation, which has two components:

1. Per-click compensation: a commission of λ ∈ (0, 1) if the consumer clicks on the link posted

by the aﬃliate.

2. Per-purchase compensation: a commission of 1 − λ if the consumer clicks on the link posted

by the aﬃliate and buys the recommended product.

That is, an aﬃliate’s payoﬀ is π

click

·λ+

purchase

·(1−λ) where

click

and

purchase

are the

indicator functions for whether the consumer clicks the aﬃliate’s link and purchases the product

recommended by the aﬃliate respectively.

2.3 The consumer

There is one consumer with unit demand who is aware of all of the products. The consumer observes

the product recommendations made by the aﬃliates, and engages in a sequential search: she can

click on a link to a product (either an aﬃliate link provided by an aﬃliate, or a link she ﬁnds

by searching a product online), evaluate and perfectly observe the product’s quality, and make

The set of N aﬃliates is presumably much smaller than the set of all aﬃliates active in the market and represents

the aﬃliates the consumer considers. These aﬃliates could be the consumer’s selection among the top results from

her search for the products on a search engine.

This approximates the case in which each aﬃliate receives signals for a large number of products, which is

nevertheless small relative to the set of all products.

The commission amount in practice is typically a fraction of the price of the product. The retailer only revises

the fraction infrequently, if at all, and hence we keep the fraction given and ﬁxed in the model.

a purchasing decision. If the consumer does not purchase the ﬁrst product she evaluates, with

(exogenous) probability q ∈ [0, 1] she can click on a second link to another product and repeat the

process.

For simplicity, we assume the consumer never clicks on a third link.

We abstract from

product pricing and vertical diﬀerentiation and assume that the consumer has a net utility of 1 if

she purchases a high quality product and −1 if she purchases a low quality product.

Evaluating a product’s quality involves reviewing product speciﬁcations and reading other con-

sumers’ reviews. We capture the eﬀort invested in learning about the product’s quality by a cost c

the consumer incurs each time she learns about a new product. Therefore, if the consumer searched

n ∈ {1, 2} products before ﬁnding a high quality product, her payoﬀ is 1 − nc. We focus attention

on small enough c so that the consumer ﬁnds it proﬁtable (in expectations) to click on a link to a

product she believes to be of high quality with probability p

or higher.

2.4 Timeline and equilibrium

To sum, the timeline of our model is as follows:

1. Nature determines products qualities.

2. Each aﬃliate j receives independent signals about the qualities of products in η

and chooses

one product to recommend. Aﬃliates make their recommendations simultaneously.

3. The consumer observes the product recommendations made by the aﬃliates and searches for

a high quality product as described above.

A strategy for aﬃliate j is a map {h, l}

→ ∆η

from quality signals for products in the set

to a (potentially stochastic) recommendation. A strategy for the consumer is a map ({0} ∪

NS)

{1,2,...,N}

→ ∆(({0} ∪ N S ∪ ∅) × ({0} ∪ NS ∪ ∅)) from the vector of the recommended products

by all of the aﬃliates to a (potentially stochastic) choice of at most two products, one that she

clicks on ﬁrst, and another that she clicks on with probability q if she didn’t purchase the product

she clicked on ﬁrst.

There are many potential reasons for the consumer to stop her search: outside distractions, fatigue, or other

time and mental constraints.

The possibility of a second click is suﬃcient to capture the eﬀect of consumer’s search length on aﬃliates’

recommendation decisions and conformity incentive, while maintaining the tractability of the model.

In fact, if c is suﬃciently large to deter the consumer from clicking on a link for a product that is of high quality

with probability p

, all equilibria of the game are such that no search takes place and no link is ever clicked.

A Perfect Bayesian Equilibrium is a collection of aﬃliates and consumer strategies and beliefs

such that each aﬃliate’s strategy maximizes his expected proﬁt, the consumer’s strategy maximizes

her expected utility, and all beliefs are consistent with Bayes law whenever possible. In what follows,

whenever we refer to an equilibrium, we mean a Perfect Bayesian Equilibrium.

2.5 Discussion of modeling assumptions

2.5.1 The commission model: pay-per-click vs. pay-per-purchase

As mentioned in the introduction, a minority of retailers and retail platforms still follow the outright

pay-per-click aﬃliate commission model. However, most, if not all, retailers who follow a pay-per-

purchase aﬃliate commission model pay an aﬃliate on any purchase made by consumers within a

relatively large time frame (the “cookie duration”), regardless of whether the consumers purchased

the products recommended by the aﬃliate. This practice provides aﬃliates with pay-per-click-like

incentives. That is, an aﬃliate has at least a component of his expected payoﬀ independent of

whether the product he recommends is purchased.

In our baseline model, we abstract from the speciﬁc implementation of the compensation oﬀered

by the retailer and capture the pay-per-click-like component by λ. One can interpret a retailer’s

commission model with a high λ as the retailer oﬀering its aﬃliates a longer cookie duration,

providing aﬃliates with greater ﬂexibility of receiving a commission beyond a sale of a linked

product. In Section 4.2, we formulate a model that explicitly captures the pay-per-purchase-with-

time-frame environment and shows how it is nested within our current model. We then apply this

formalization to analyze the retailer’s choice of aﬃliates’ compensation model.

2.5.2 Single salient product

For tractability, we assume throughout that there is one salient product. While we expect many

of our results to extend to an environment with multiple salient products, such an environment

may also introduce the possibility of additional forms of conformity.

We leave the investigation

of other conformity equilibria in a richer model for future research.

For example, one strong form of conformity will be one in which aﬃliates’ establish an ordering of the salient

products, such that all aﬃliates who receive a high signal for product ‘a’ recommend it, all aﬃliates who receive a

low signal for product ‘a’ and a high signal for product ‘b’ recommend product ‘b’, and so forth. The sustainability

of some of these conformity strategy proﬁles in equilibrium might require the model to allow the consumer’s longer

search duration accordingly.

2.5.3 Informed consumer

We assume that once the consumer evaluates a product, she will perfectly learn the product’s

quality. We relax this assumption and explore the eﬀect of the consumer’s ability to self-evaluate

products in Section 4.1. We show that our results extend qualitatively to this more general case

and derive new insights from emerging quantitative changes.

3 Results: conﬂict of interest and aﬃliates’ conformity

Due to the nature of the coordination game between aﬃliates and the asymmetric information

between aﬃliates and the consumer, our model admits a large set of equilibria, including some less

interesting (or realistic) ones in which some (or all) products are never recommended and never

purchased with corresponding ad-hoc beliefs over zero probability events. Therefore, instead of

characterizing the entire set of equilibria, we ﬁrst show that two aﬃliates’ strategy proﬁles stand

out because, for any set of parameters, one of the two strategy proﬁles always maximizes aﬃliates’

and/or the consumer’s payoﬀs. These two strategy proﬁles are polar opposites, and their optimality

highlights an inherent conﬂict of interest in this market. Then, we characterize the range of market

parameters for which each of the two strategy proﬁles is an equilibrium, highlighting important

trade-oﬀs and ineﬃciencies.

3.1 Conﬂict of interest

Our ﬁrst result characterizes the inherent conﬂict of interest between the aﬃliates as a group and

the consumer with respect to recommendations of salient versus non-salient products and how it

depends on the length of consumer search and on aﬃliates’ compensation. Two aﬃliates’ strategy

proﬁles emerge as important in our analysis.

Deﬁnition 1. A conformity strategy proﬁle is a strategy proﬁle in which every aﬃliate who receives

a high signal for the salient product recommends it and every aﬃliate who receives a low signal

for the salient product recommends a non-salient product for which he received a high signal. A

conformity equilibrium is an equilibrium in which aﬃliates employ a conformity strategy proﬁle.

A non-conformity strategy proﬁle is a strategy proﬁle in which, regardless of their signals for

the salient product, every aﬃliate recommends a non-salient product for which he received a high

signal. A non-conformity equilibrium is an equilibrium in which aﬃliates employ a non-conformity

strategy proﬁle.

Proposition 1. Suppose the consumer best responds given the aﬃliates’ strategy proﬁle (and some

beliefs that are consistent with the Bayes’s rule given the aﬃliates’ strategy proﬁle).

Then,

(1) a conformity strategy proﬁle maximizes the consumer’s expected payoﬀ among all aﬃliates’

strategy proﬁles;

(2) If λ ≥

1−p

1+q−p

, then a non-conformity strategy proﬁle maximizes the aﬃliates’ aggregate

expected payoﬀ among all aﬃliates’ strategy proﬁles; otherwise, a conformity strategy proﬁle

maximizes the aﬃliates’ aggregate expected payoﬀ among all aﬃliates’ strategy proﬁles.

Proposition 1 delivers a bang-bang result: depending on the parameters of our model, the

aﬃliates and the consumer may have completely aligned interests or completely opposite interests

(but nothing in between) on whether aﬃliates recommend the salient product when they receive a

positive signal on its quality.

Part (1) of Proposition 1 shows that regardless of the parameters of the model, the consumer

beneﬁts from aﬃliates’ conformity. Intuitively, aﬃliates’ conformity allows the consumer to have

more accurate information on at least one product (the salient product). This increases the proba-

bility that the ﬁrst product that the consumer clicks on is of high quality, leading to: (1) a shorter

and less costly search, and (2) a higher probability of the search ending with a purchase of a high

quality product.

Note that the condition λ ≥

1−p

1+q−p

in part (2) of Proposition 1 can be equivalently expressed

as p

≥

1−λ−λq

q−λq

, or q ≥

1−λ

λ+p

−λp

. Therefore, aﬃliates’ total expected payoﬀs are the highest under

non-conformity, if: (1) a signiﬁcant fraction of aﬃliates’ compensation is per-click, (2) the consumer

is likely to continue searching after a click that doesn’t lead to a purchase, and (3) aﬃliates receive

suﬃciently accurate signals on products’ qualities. In this case, the consumer and the aﬃliates

have opposing interests.

This is akin to a hypothetical scenario in which aﬃliates’ strategy proﬁle can be exogenously determined and

publicly announced and the consumer best responds to it.

Note also that

1−λ−λq

q−λq

> 1 if and only if 1 − λ > q, or λ + q < 1. It follows that, if λ + q < 1, then

1−λ−λq

q−λq

> p

for all p

≤ 1, that is, the condition in part (2) of Proposition 1 cannot hold. Therefore, if a suﬃciently large fraction

of aﬃliates’ compensation is per-purchase (low λ) or if the consumer’s search is suﬃciently short (low q). Aﬃliates

(as a group) have aligned interests with the consumer regardless of the aﬃliates’ information accuracy p

Intuitively, when aﬃliates are compensated signiﬁcantly per click, and when it is likely that the

consumer will continue clicking after not purchasing, the average expected payoﬀ for an aﬃliate

increases in the expected length of the consumer’s search. At the same time, as long as aﬃliates’

compensation does not put signiﬁcant weight on the purchase, aﬃliates’ expected payoﬀs are not

reduced much if the search is likely not to end in a purchase. Conversely, suppose aﬃliates are

compensated mainly per purchase, and the consumer is expected to stop searching after an unsuc-

cessful ﬁrst click. In that case, aﬃliates’ interests align with the consumer’s preference for aﬃliates’

conformity. Figure 1 captures these observations.

The eﬀect of the accuracy of the aﬃliates’ signals is more subtle. A high accuracy signal implies

that the search will likely end in purchase even if aﬃliates do not conform to their recommendations,

thus making the non-conformity outcome better for aﬃliates. This eﬀect is more substantial when

a larger fraction of aﬃliates’ compensation is per purchase and the probability that the consumer

continues searching after one low-quality product is high. We can see this eﬀect by comparing the

contour lines in Figure 1.

Figure 1: Aﬃliates’ preference for conformity

For three values of p

, the ﬁgure illustrates a partition of the q-λ space that distinguishes

when aﬃliates prefer conformity (vs. non-conformity). Aﬃliates’ aggregate payoﬀ is

highest under conformity when aﬃliates are compensated heavily per-purchase (small λ)

and consumer search is short (small q). In contrast, aﬃliates’ aggregate payoﬀ is highest

under non-conformity when aﬃliates are compensated heavily per-click (large λ) and

consumer search is long (large q). If aﬃliates signals are more accurate (large p

) the

range of parameters for which aﬃliates’ aggregate payoﬀ is highest under conformity is

smaller. (In the ﬁgure N = 10.)

3.2 Equilibrium and aﬃliates’ conformity

We now analyze the conditions under which aﬃliates’ conformity and non-conformity can be sup-

ported as equilibrium outcomes. We ﬁrst show that regardless of the parameters of the model, there

exists a non-conformity equilibrium, i.e., an equilibrium in which no aﬃliate ever recommends the

salient product.

Proposition 2. There always exists a non-conformity equilibrium.

Proposition 2 provides bad news for the consumer, whose payoﬀ is maximized under aﬃli-

ates’ conformity. Proposition 2 suggests that aﬃliates’ non-conformity can emerge in equilibrium

regardless of the parameters of the model. When combined with Proposition 1, Proposition 2 pro-

vides good news to the aﬃliates when aﬃliates’ payoﬀs have a signiﬁcant per-click component or

consumers are more likely to continue their search beyond the ﬁrst click.

To gain intuition for Proposition 2, it is useful to consider the case that the consumer follows

exactly two aﬃliates. In this case, essentially all equilibria are non-conformity equilibria.

gain intuition into why when N = 2 this equilibrium is unique, consider an equilibrium candidate

in which any aﬃliate who receives a good signal for the salient product recommends the salient

product with some positive probability. Assume by contradiction that this is an equilibrium. Then,

if one aﬃliate recommends the salient product and one doesn’t, this informs the consumer that one

of them received a good signal for the salient product and the other, at least with some positive

probability, received a negative signal for the salient product. As a result, the consumer’s posterior

puts a higher probability that the recommended non-salient product is of high quality than that

the salient product is high quality. If such an equilibrium exists, the only situation in which the

consumer will click the salient product is if both aﬃliates recommend the salient product. However,

in that case, each of the aﬃliates can deviate to recommend a non-salient product and receives the

consumer’s click with probability 1.

When N > 2, additional equilibria may exist. Motivated by Proposition 1, which tells us that a

conformity equilibrium maximizes the consumer’s payoﬀs and sometimes maximizes also aﬃliates’

payoﬀs (and thus aggregate social welfare), our next result characterizes the set of parameters for

which aﬃliates’ conformity is an equilibrium.

Proposition 3. Fix any N > 2. For any q, λ there exist

≤ p ≤ ¯p < 1 such that:

(1) for every p

> ¯p, there exists a conformity equilibrium; and

(2) for every p

< p, a conformity equilibrium does not exist.

The intuition for Proposition 3 is most straightforward when considering N large yet ﬁnite. That

is, the consumer observes the recommendations of a large (ﬁnite) number of aﬃliates: Consider

aﬃliate j, and suppose that the quality of the salient product is high and all other aﬃliates act

according to the conformity strategy proﬁle, that is, if they receive a positive signal on the salient

There is only one additional equilibrium in which at most one aﬃliate recommends the salient product. This

equilibrium is equivalent to a non-conformity equilibrium in the sense that no one product is ever recommended by

two aﬃliates in equilibrium.

Moreover, for any 0 ≤ λ ≤ 1, there exists a unique ˆq ∈ (0, 1) such that for any q ̸= ˆq, the upper bound p(q, λ)

for the range of p

on the non-existence of a conformity equilibrium is strictly larger than

. Therefore, generically,

the proposition can be re-written with strict inequalities

< p ≤ ¯p < 1 and we can say that generically for any

0 ≤ q ≤ 1 and 0 ≤ λ ≤ 1 there exists ranges of p

in which a conformity equilibrium exists and ranges of p

in which

a conformity equilibrium does not exist.

product they post a recommendation for it. Then, there is a considerable probability that the salient

product gets most of the recommendations observed by the consumer. This probability increases

in the accuracy of the aﬃliates’ signals, p

. As p

approaches 1, the probability that conditional on

being high quality, the salient product gets an overwhelming majority of the recommendations is

high. In that case, the consumer clicks ﬁrst on a link to the salient product with high probability,

and because the salient product is of high quality, the consumer will not search further. Therefore, to

have a chance of having his link clicked on, aﬃliate j would need to recommend the salient product

when the salient product is of high quality. It is just left to note that, for a high information

accuracy p

, the probability that the salient product is of high quality conditional on aﬃliate j

receiving a positive signal is high.

When considered in tandem with Proposition 1, Proposition 3 carries two main welfare impli-

cations. First, even when both the consumer and the aﬃliates would beneﬁt from the aﬃliates’

conformity, a conformity equilibrium may not exist, leading to a sub-optimal equilibrium outcome.

This sub-optimal outcome occurs, for example, when aﬃliates’ signals are suﬃciently inaccurate.

Second, even when aﬃliates as a group prefer non-conformity, a conformity equilibrium may

exist. For example, part 1 of Proposition 3 tells us that a conformity equilibrium exists if aﬃliates

receive suﬃciently accurate product quality signals. However, Proposition 1 tells us that this is the

case in which the aﬃliates can maximize their aggregate payoﬀs when they never recommend the

salient product. Notably, a conformity equilibrium is always ideal for the consumer. We illustrate

these two welfare implications in Figure 2.

Figure 2: Conformity-driven ineﬃciency

Below the dark blue dashed line (regions I, III, and V), aﬃliates achieve the maximal

aggregate payoﬀ under aﬃliates’ conformity, whereas above the dashed line (regions II,

IV, and VI), aﬃliates achieve maximal aggregate payoﬀ under their non-conformity. Be-

tween the two solid lines (regions II and III), a conformity equilibrium exists. In regions

I and IV, a conformity equilibrium does not exist due to aﬃliates’ too strong incentive to

recommend the salient product even after they learn it is of low quality. In regions V and

VI, a conformity equilibrium does not exist due to too-strong incentives to recommend

the non-salient product. In region I (shaded with solid grey), a conformity equilibrium

does not exist, but both the consumer and the aﬃliates achieve the maximal payoﬀs

under aﬃliates’ conformity. In region II (shaded with dots), a conformity equilibrium

exists, but aﬃliates can maximize their aggregate payoﬀ from non-conformity. (In the

ﬁgure N = 10, p

= 0.57.)

We can say more.

Corollary 1. Let ¯p

(q, λ) be the lowest signal accuracy above which there always exists a conformity

equilibrium, i.e., ¯p

(q, λ) := min{¯p(q, λ)}. Then,

(1) there exist 0 < q ≤ q < 1 such that if q < q, then p

(q, λ) is decreasing in λ, and if q > q,

then p

(q, λ) is increasing in λ;

(2) for any λ, there exist 0 < q ≤ q < 1 such that if q < q, then p

(q, λ) is decreasing in q, and

if q > q, then p

(q, λ) is increasing in q.

Corollary 1 shows that the expected length of the consumer’s search and the aﬃliates’ com-

pensation scheme have non-monotonic eﬀects on the existence of a conformity equilibrium. As

a result, a conformity equilibrium is most likely to exist if the aﬃliate compensation scheme is

between per-click and per-purchase compensation and when consumers’ search is of intermediate

length. This assertion is interesting because, as mentioned in the introduction, in recent years,

aﬃliate programs have converged on an aﬃliate compensation scheme that is eﬀectively between

per-click and per-purchase compensation.

To better understand the source of this non-monotonicity, assume that all aﬃliates employ

conformity strategies and consider the following two conceivable unilateral deviations: (1) an af-

ﬁliate who receives a high-quality signal for the salient product may, nevertheless, recommend a

non-salient product, and (2) an aﬃliate who receives a low-quality signal for the salient product

may, despite his signal, recommend the salient product.

Consider part (2) of Corollary 1. An increase in the expected duration q of the consumer’s

search makes deviation (1) more proﬁtable and deviation (2) less proﬁtable. So much so that when

the search duration is short, there is no p

for which deviation (1) is viable. Hence, when the search

duration is short, the range of p

for which any proﬁtable deviation exists reduces in the search

duration. Once the search duration is suﬃciently high, deviation (2) is no longer viable, but for

suﬃciently low p

, deviation (1) is. In this range of q, the range of p

for which any proﬁtable

deviation exists widens in the search duration. This eﬀect is captured by part (2) of Corollary 1

and illustrated in Figure 3.

Figure 3: Existence of conformity equilibrium

In region A, a conformity equilibrium exists. In regions B and C a conformity equilibrium

does not exist: in region B this is due to too-strong incentives to recommend the salient

product (even when an aﬃliate receives a bad signal for it), whereas in region C this

is due to too-strong incentives to recommend the non-salient product. (In the ﬁgure

λ = 0.5, N = 10.)

The intuition for part (1) of the corollary follows a similar logic. An increase in the per-

click compensation, λ, make deviation (1) more proﬁtable because it reduces the importance of

recommending a product that will be purchased (recalls that the salient product, if clicked on,

is more likely to be purchased). For the same reason, an increase in λ also makes deviation (2)

less proﬁtable (more generally, it increases the expected proﬁt from recommending a non-salient

product vis-a-vis the salient product). Therefore, as part (1) of the corollary shows, an increase in

λ has the opposite eﬀect on p

when the conformity equilibrium is threatened by the possibility of

deviation (1) versus when it is threatened by deviation (2).

4 Discussion: extensions and broader implications

In this section, we ﬁrst show that our model is robust to the case in which the consumer does not

observe the quality of a product directly after clicking on an aﬃliate link. We derive implications for

the case of experience goods. We then consider the platform’s problem: optimal design of aﬃliate

incentives. We show that whether the platform prefers to put heavier weight on per-purchase vs.

per-click compensation depends on how good the platform is at converting clicks to purchases and

on the consumer’s expected search duration. We conclude by providing managerial implications.

4.1 Experience goods and the role of aﬃliates

In our baseline model we assumed that once a consumer clicks on a link to a product, she observes

the product’s quality accurately. As a result, aﬃliates had the role of inﬂuencing the consumer’s

search without having an eﬀect on whether a consumer purchases a product after she viewed

it. While this assumption provides a reasonable approximation for many product markets, some

products require the consumer to purchase before learning the quality accurately. In such cases,

the consumer may take into account the aﬃliate’s recommendations in her purchase decision even

after viewing the product page.

We now consider a more general model in which the consumer observes some information about

the product in the form of a potentially noisy signal. Formally, suppose that after the consumer

clicks an aﬃliate link for product i ∈ {0} ∪ NS, she observes a signal ˜s(i) ∈ {

l} such that

P r(˜s(i) =

h|q

= H) = P r(˜s(i) =

l|q

= L) = π

> 1/2. We assume that the consumer’s signal is

conditionally independent from those of the aﬃliates. The aﬃliates’ information, the payoﬀs for

the aﬃliates and the consumer, and the timing of the game remain the same as in our baseline

model (Section 2).

We ﬁnd all our results for the baseline model hold.

Proposition 4. In the model in which the consumer observes a signal from clicking on an aﬃliate’s

link:

(1) (Proposition 1) A conformity strategy proﬁle maximizes the consumer’s expected payoﬀ among

all aﬃliates’ strategy proﬁles.

(2) (Proposition 1) If λ >

1−p

1+q−p

, then a non-conformity strategy proﬁle maximizes the aﬃliates’

aggregate expected payoﬀ among all aﬃliates’ strategy proﬁles; otherwise, a conformity strategy

proﬁle maximizes the aﬃliates’ aggregate expected payoﬀ among all aﬃliates’ strategy proﬁles.

(3) (Proposition 2) There always exists a non-conformity equilibrium.

(4) (Proposition 3) Fix any N > 2, there exist

< p

′

≤ p

′′

< 1 such that, for all q, λ:

(a) for every p

> p

′′

, there exists a conformity equilibrium;

(b) for every p

< p

′

, a conformity equilibrium does not exist.

An interesting special case is the case of experience goods—goods on which the consumer obtains

no quality signal before trying out the good.

This is captured by the limit case in which the

consumer observes an uninformative signal, i.e., π

= 1/2. For this case we can say more.

Corollary 2. In the model of experience goods:

(1) both conformity and non-conformity strategy proﬁles maximize the aﬃliates’ aggregate ex-

pected payoﬀ among all strategy proﬁle.

(2) aﬃliate compensation (λ) and the length of consumer search (q) do not aﬀect the range of

aﬃliate signal accuracy level (p

) for which a conformity equilibrium exists.

An immediate broader implication of this observation is that in markets for experience goods,

the retailer cannot aﬀect equilibrium behavior via aﬃliate compensation.

The intuition behind Corollary 2 begins by noting that this scenario is mathematically equivalent

to our baseline model when parameters’ values are set to λ = 1 and q = 0. To see why, note that

for every strategy proﬁle pursued by the aﬃliates, the consumer’s unique best response is to click

on the link to a product that has the highest posterior probability of being high quality and to

purchase that product. That is, any aﬃliate’s expectation of being clicked on is identical to our

baseline model in which the consumers clicks only once (q = 0). The aﬃliate then expects to be

paid λ + (1 − λ) = 1 if his link is clicked on by the consumer, but the probability of purchase

conditional on clicking is 1, and therefore identical to what he’s paid in our baseline model when

λ = 1.

4.2 Platform’s design

So far we have treated the aﬃliate compensation scheme as exogenous. In reality, however, every

online retailer has the ability to design the compensation scheme of its aﬃliate program. In the

early days of e-commerce, formal pay-per-click compensations schemes were common. The rise of

Many personal services fall into this category (e.g. restaurant, hairdresser, beauty salon, theme park, travel,

holiday).

bots and click-fraud led many retailers to change their compensation model to pay-per-purchase,

in order to guarantee that paid clicks arrive from real consumers.

However, as suggested in Section 2.5.1, a large component of the compensations scheme of many

aﬃliate programs is still in expectations in the form of pay-per-click compensation. Aﬃliate pro-

grams achieve that by paying aﬃliates for any purchase of the consumer within a predetermined

time-frame after the click. The longer the time-frame the larger the expected share of compensation

coming from per-click-like payments (relative to per-purchase). Additional platform design con-

sideration that increase the eﬀective per-click compensation are larger product variety and better

platform internal recommendation system, as they increase the probability that a consumer buys

something on the platform.

We capture the platform’s objective within our model as follows: Let r be the probability that,

conditional on clicking, the consumer buys a diﬀerent product on the platform, and let v be the

expected sale price of that product. Normalize the sale price of the product recommended by the

aﬃliate to 1. Finally, let ρ be the commission in terms of the fraction of the sale price paid to the

aﬃliate.

The expected payoﬀ for the aﬃliate, conditional on the consumer clicking on his recommenda-

tion, can be written as

ρ · (Pr(consumer buys the aﬃliate-recommended product conditional on clicking) + r · v).

By varying the time frame for compensation and its recommendation algorithm the platform

changes r (and maybe also v) and thus the relative weights given to pay-per-click vs. pay-per-

purchase in the aﬃliate’s compensation scheme. We note that this compensation scheme is captured

by our modeling above when ρ is normalized so that ρ + r · v · ρ = 1.

We denote by P

the probability that the platform sells a product recommended by an aﬃliate in

a conformity equilibrium and by P

the probability of such a sale in a non-conformity equilibrium.

To see how, set λ = r · v · ρ and note that by the normalization 1 − λ = ρ. Moreover, because the normalization

does not aﬀect any of our results above, the platform can always change ρ without aﬀecting the equilibrium—the

only restriction is that ρ is suﬃciently high so that, in equilibrium, aﬃliates’ expected incomes are such that they

stay active. Since the platform can modify ρ it will then pay aﬃliate the lowest total payoﬀ to keep them active and

can adjust the compensation structure to the equilibrium played so that it delivers to aﬃliates the same minimal

expected payoﬀ. Thus, without loss of generality, we can focus on the platform’s choice of λ (through its choice

of policies aﬀecting r, such as the time frame considered for aﬃliate compensation), and assume that the platform

chooses ρ to maximize its revenues.

We denote by τ the additional expected revenue to the platform from a click directed to it by

an aﬃliate, and by x

and x

the expected number of clicks in a conformity and non-conformity

equilibrium respectively.

Let E ∈ {c, nc}. The platform’s revenue is then captured by

= P

+ x

· τ (1)

Next, note that our analysis above (Proposition 1) shows that P

≥ P

. On the other hand, the

same analysis shows that x

≤ x

. Therefore, holding all else equal, a platform that converts a

click into higher revenues (high τ ) will prefer a non-conformity equilibrium, whereas a platform

that does not converts clicks into high revenues will prefer a conformity equilibrium.

In addition, as we showed in Section 4.1, for a platform selling experience goods x

= x

, and

such a platform, therefore, will always prefer a conformity equilibrium.

The remaining question is then, how can a platform aﬀect whether a conformity or non-

conformity equilibrium is played. Due to the multiplicity of equilibria the platform may not be

able to deterministically aﬀect which equilibrium is played. However, it can aﬀect whether a con-

formity equilibrium exists or not. Corollary 1 provides guidelines to a platform seeking to aﬀect

the existence of a conformity equilibrium. In particular,

1. If the consumer’s search is expected to be short (low q), the platform can make conformity

equilibrium exist (not exist) by increasing (decreasing) the share of compensation paid per-

click (λ).

2. If the consumer’s search is expected to be long (high q), the platform can make conformity

equilibrium exist (not exist) by decreasing (increasing) the share of compensation paid per-

click (λ).

4.3 Managerial implications

This paper provides managerial implications for aﬃliates, brands, and platforms alike.

Aﬃliates

If aﬃliates have accurate signals of products’ qualities, they will beneﬁt the most under a non-

conformity equilibrium, which always exists. Therefore, aﬃliates can beneﬁt from coordinating

on a non-conformity equilibrium. However, this is the scenario in which a conformity equilibrium

also exists, which makes aﬃliates’ coordination on a non-conformity strategy proﬁle tricky because

consumers prefer a conformity equilibrium. A well-informed regulator might try to crack down on

such attempts.

In contrast, if aﬃliates’ signals are less accurate, they will beneﬁt from conformity. Unfortu-

nately, this is the scenario in which a conformity equilibrium may not exist, to the detriment of

the aﬃliates and the consumers. All parties in this case (except non-salient brands) will beneﬁt

from increasing the availability of accurate information to all aﬃliates. Improving the accuracy

of aﬃliates’ product quality information can be done, for example, by a salient brand or platform

providing samples to aﬃliates (more on that below) or by aﬃliates investing more intensively in

gathering information.

In markets for experience goods, in which consumers do not receive quality signals indepen-

dent of aﬃliates’ recommendations, aﬃliates are indiﬀerent between conformity and non-conformity

equilibria. Because consumers prefer conformity equilibria, if aﬃliates engage in conformity equi-

librium, more consumers will be attracted to the market, ultimately beneﬁting all parties.

Brands

When aﬃliates receive inaccurate signals about product quality, a conformity equilibrium does

not exist. Therefore, the salient brand may want to make accurate quality information readily

accessible as it will make it more likely that a conformity equilibrium exists. Interestingly, this is

consistent with salient brands sending samples to inﬂuencers with no conditions on how favorable

their reviews will be.

Platforms

Even while paying per-purchase to avoid click fraud, platforms can balance between per-purchase

compensation and per-click compensation. Shortening the time window for purchase and intro-

ducing a policy that only the latest clicked-on aﬃliate is compensated for purchases (the “last

click wins” model) reduce the “per-click” weight in aﬃliate compensation. Improvements in the

matching and recommendations algorithms of a platform, increase in the scope of products carried

by a platform, and general price competitiveness and consumer loyalty to the platform increase the

“per-click” weight in the compensation.

Whether the platform prefers a conformity or non-conformity equilibrium depends on the plat-

form’s ability to extract additional unrelated purchases from a click. A platform with a good in-site

recommendation system and a large variety of product categories, such as eBay or Amazon, may

prefer to maximize clicks and, therefore, encourage a non-conformity equilibrium, perhaps by set-

ting the compensation scheme in a way that will not admit a conformity equilibrium. On the other

hand, a platform with a less established recommendation system or a more specialized platform

with a narrow focus is likely to prefer a conformity equilibrium, which increases the probability of

purchase.

If consumers are expected to conduct longer searches, a platform seeking to facilitate a confor-

mity equilibrium will look for a per-purchase compensation scheme. The reverse is true if consumers

conduct shorter searches on average. In contrast, when consumers cannot learn about the prod-

uct quality independently of the aﬃliates’ recommendations, the platform’s aﬃliate compensation

scheme does not aﬀect equilibrium behavior and whether salient or non-salient products are sold

in equilibrium.

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Appendix: Proofs of Sections 3 and 4

Proof of Proposition 1. We ﬁrst use the ex ante homogeneity across the non-salient products to

simplify the consideration of aﬃliates’ strategy spaces. Because any two non-salient products

are ex ante identical, if an aﬃliate j receives high signals for two non-salient products, then any

probability distribution of recommendations between the two induces the same outcome. That

is, for any i

, i

∈ η

, with i

, i

̸= 0 and s

) = s

) = h, all of the strategies for aﬃliate j

holding P r(recommend i

) + P r(recommend i

) constant induce the same outcome. Therefore, for

the consideration of payoﬀs, it suﬃces to pick a representative from each set of strategies with the

same total probability of recommending non-salient products—one that allocates that probability

entirely to one non-salient product. As a result, we are reduced to consider the following set of

strategies for each aﬃliate j: (α

, β

) ∈ [0, 1], where α

and β

represent the probabilities aﬃliate j

will recommend product 0 contingent on his signal about it. That is, with probability α

, aﬃliate j

will recommend product 0 after a high signal about product 0, and with probability (1−α

), he will

recommend a non-salient product for which he receives a high signal; with probability β

, aﬃliate

j will recommend product 0 after a low signal about product 0, and with probability (1 − β

), he

will recommend a non-salient product for which he receives a high signal.

Denote by P r



H|0

(n)



the consumer’s posterior belief of product 0 being of high quality

when she sees n recommendations for product 0. Being a risk-neutral expected utility maxi-

mizer, the consumer’s best response in her search to a strategy proﬁle for the aﬃliates is: (1) when

P r



H|0

(n)



≥ p

, search product 0 ﬁrst, if it is of high quality, stop the search and make a purchase

of one unit of product 0, otherwise (with probability q) search a non-salient product among the

recommended ones; when P r



H|0

(n)



< p

, search any non-salient product that is recommended

ﬁrst, if it is of high quality, stop and make a purchase of the searched product, otherwise, (with

probability) search another recommended non-salient product. Therefore, the consumer’s expected

utility is

E[U(q)|n] =











(1 − c)p

+ (1 − 2c)(1 − p

q if P r



H|0

(n)



< p

(1 − c)P r



H|0

(n)



+ (1 − 2c)



1 − P r



H|0

(n)



q otherwise

(2)

Collecting P r



H|0

(n)



in the later case, we have

(1 − c)P r



H|0

(n)



+ (1 − 2c)



1 − P r



H|0

(n)



q = [1 − p

q − c(1 − 2p

q)]P r



H|0

(n)



+ (1 − 2c)p

The expression above is linear in P r



H|0

(n)



, whose coeﬃcient 1 − p

q − c(1 − 2p

q) must be

positive. This is because when 1 − 2p

q < 0, then clearly it is positive; and when 1 − 2p

q > 0,

1 − p

q > 1 − 2p

q > c(1 − 2p

q), so it is positive as well. Therefore, consumer’s expected utility is

bounded from below by that when she only considers non-salient products and attains its maximum

when her posterior about product 0 is at the highest, conditional on the number of recommendations

for product 0 is high enough for her to consider product 0 ﬁrst.

To prove part (1) of the proposition, it is suﬃcient to show that the conformity strategy proﬁle

maximizes the consumer’s posterior belief about product 0’s quality conditional on the number of

recommendations it receives.

Suppose that the aﬃliates have chosen the strategy proﬁle represented by {(α

, β

)}

j=1,...,N

Let n ≤ N be the number of recommendations for product 0 the consumer observes. To streamline

notations, we deﬁne the following partitions on the set of aﬃliates. Let H(n) (L(n), resp.) be the

set of aﬃliates who receive high signals (low signals, resp.) about product 0, such that |H(n)| =

≤ N and |L(n)| = N − N

. Furthermore, let H

(n) ⊂ H(n) (L

(n) ⊂ L(n), resp.) denote the

set of aﬃliates who choose to recommend product 0. Then by deﬁnition, |H

(n)| + |L

(n)| = n.

First, the probability that product 0 receives n recommendations conditional on that N

aﬃli-

ates received high signals about it is

P r



(n)

|(h

, l

N−N

)



m=1





N − N

n − m



j∈H

(n)

(n)|=m

g ∈H(n)\H

(n)

(1−α

)

k∈L

(n)

l∈L(n)\L

(n)

(1−β

(3)

Next, as the number N

of high signals for product 0 ranges from n to N, the probability that

product 0 will receive n recommendations conditional on its true quality is

P r



(n)



P r



, l

N−N

)|H



P r



(n)

|(h

, l

N−N

)



, (4)

P r



(n)



P r



, l

N−N

)|L



P r



(n)

|(h

, l

N−N

)



. (5)

where the probabilities that product 0 receives N

high signals and N − N

low signals conditional

on its true quality are

P r



, l

N−N

)|H







(1 − p

)

N−N

, (6)

P r



, l

N−N

)|L







(1 − p

)

N−N

. (7)

Given that the prior quality for product 0 being high or low is equally likely, by Bayes’s Rule, the

consumer’s posterior belief that product 0 is of high quality is

P r



H|0

(n)



P r



(n)



P r



(n)



+ P r



(n)



. (8)

By eqs. (6) and (7), the distribution of signals about product 0 received by the aﬃliates is

independent of the aﬃliates’ strategies, and hence, we are reduced to maximize the conditional

probabilities P r



(n)

|(h

, l

N−N

)



given by eq. (3). By the symmetry between the α

’s and β

’s,

and because p

> 1/2, it is without loss of generality to assume α

≥ β

for j = 1, . . . , N. Note

that when 0 ≤ β

≤ α

≤ 1, the expression

j∈H

(n)

(n)|=m

g∈H(n)\H

(n)

(1 − α

)

k∈L

(n)

l∈L(n)\L

(n)

(1 − β

) ≤ 1,

and it attains maximum value of 1 when either

(1) (α

, β

) = (1, 1) for j = 1, . . . , N, requiring H

(n) = H(n) and L

(n) = L(n); or

(2) (α

, β

) = (1, 0) for j = 1, . . . , N.

However, the ﬁrst situation above is only possible when N

= N, i.e., the entire group of aﬃliates

all receive high signals about product 0. It is hence non-generic. When (α

, β

) = (1, 0) for

j = 1, . . . , N, necessarily, m = n = N

, implying that the number of recommendations for product

0 that the consumer sees coincides with the number of aﬃliates who received high signals about

product 0. Therefore, we have shown the strategy proﬁle speciﬁed as (α

, β

) = (1, 0) for j =

1, . . . , N maximizes the consumer’s expected utility from best responding to this strategy proﬁle.

This completes the proof of part (1).

To prove part (2), suppose that the aﬃliates act according to a strategy proﬁle characterized

by {(α

, β

)} for j = 1, . . . , N, yielding n recommendations for product 0. Then the aﬃliates’ total

expected payoﬀ is

EU(α, β) = λ

1 + q



1 − max

, P r



H|0

(n)

oi

+ (1 − λ)

max

, P r



H|0

(n)

o

+ p



1 − max

, P r



H|0

(n)

oi

. (9)

Collecting max



, P r



H|0

(n)



, we can express eq. (9) as

EU(α, β) = [1 − p

q − (1 + q − p

q)λ] · max

, P r



H|0

(n)

o

+ p

q + (1 + q − p

q)λ. (10)

Note that the aﬃliates’ total expected payoﬀ is linear in max



, P r



H|0

(n)



. Therefore, EU(α, β)

attains its maximum when max



, P r



H|0

(n)



= p

if 1 − p

q − (1 + q − p

q)λ < 0, and when

max



, P r



H|0

(n)



= P r



H|0

(n)



is at its highest if 1 − p

q − (1 + q − p

q)λ ≥ 0. The sign

of the expression 1 − p

q − (1 + q − p

q)λ induces the aﬃliates’ preference dichotomy. When

1 − p

q − (1 + q − p

q)λ ≤ 0, the aﬃliates want to maximize the probability that P r



H|0

(n)



≤ p

across all possible realized recommendation proﬁles, which will be fulﬁlled by a non-conformity

proﬁle. To the contrary, when 1 − p

q − (1 + q − p

q)λ ≥ 0, the aﬃliates want to maximize the

probability that P r



H|0

(n)



≥ p

, which will be achieved by a conformity proﬁle. This completes

the proof of part (2).

Proof of Proposition 2. Consider the following strategies: all aﬃliates recommend non-salient prod-

ucts regardless of their signals for product 0. The consumer follows only recommendations for no-

salient products. It is immediate that the aﬃliates’ strategies are best responses to the consumer’s

strategy. Given that the probability that an aﬃliate recommends the salient product is zero, the

consumer’s strategy can be supported as best response to the aﬃliates’ strategies with the following

beliefs: if an aﬃliate recommends product zero it is a mistake, which is equally likely when the

aﬃliate receives a high or low signal for the salient product.

Proof of Proposition 3. (1) We verify that a conformity strategy proﬁle constitutes a pure-strategy

equilibrium in the extreme scenario when p

= 1 by checking the non-proﬁtability for any aﬃliate

from a unilateral deviation. Then part (1) of Proposition 3 follows by the continuity of an aﬃliate

j’s expected payoﬀ in p

Case 1. Aﬃliate j observes a high signal s

(0) = h for product 0.

When p

= 1, P r



, l

N−1−k

)|s

(0) = h



= 1 if k = N − 1 and 0 otherwise. That is, when

the signal about product quality is perfectly informative, one aﬃliate’s high signal about product

0 implies all the other aﬃliates also received high signal about product 0. When all other aﬃliates

use a conformity strategy, they will all elect to recommend product 0. Then,

E[U

(0|s

(0) = h), p

= 1] =

> E[U

(j|s

(0) = h, s

(i) = h), p

= 1] = 0. (11)

Case 2. When aﬃliate j observes a low signal s

(0) = l. When p

= 1, recommending product

0 yields aﬃliate j a lower expected payoﬀ than recommending a non-salient product i:

E[U

(0|s

(0) = l, p

= 1)] = 0 < E[U

(j|s

(0) = l, s

(i) = h, p

= 1)] =

. (12)

Note that aﬃliate j’s expected utilities following any strategy when all the other aﬃliates use

the strategy (α

, β

) = (1, 0) for any l ̸= j are continuous in p

for

< p

≤ 1. Then, there exists

some

≤ ¯p(q, λ) < 1 such that aﬃliate j ﬁnds no proﬁtable deviation from (α

, β

) = (1, 0) when

¯p(q, λ) < p

≤ 1. This completes the proof of part (1).

(2) We show that ¯p

(q, λ) >

except at one point. We consider the limits of aﬃliate j’s

expected utilities as p

approaches

. When p

, product 0 needs

recommendations for the

consumer to consider ﬁrst when N is even, and

N+1

recommendations when N is odd.

Since aﬃliate j’s expected utility from recommending a non-salient product is strictly increasing

in q for any

< p

< 1 when s

(0) = h, there exists ˆq such that

lim

→

(

)

E[U

(0|s

(0) = h)|q > ˆq] < lim

→

(

)

E[U

(j|s

(0) = h, s

(i) = h)|q > ˆq], (13)

lim

→

(

)

E[U

(0|s

(0) = l)|q < ˆq] > lim

→

(

)

E[U

(j|s

(0) = l, s

(i) = h)|q < ˆq]. (14)

The reason that the same ˆq can serve as the cutoﬀ for both inequalities (13) and (14) is that as

→





, aﬃliate j’s expected utility is independent from his signal about product 0. Therefore,

when the probability of a second click by the consumer becomes suﬃciently high, and when the

signal informativeness becomes suﬃciently low, and when all the other aﬃliates follow the strategy

(α

, β

) = (1, 0), aﬃliate j ﬁnds it more proﬁtable to recommend a non-salient product than product

0 after receiving a high signal about product 0. Therefore, for any given q (keeping λ and N ﬁxed

throughout) and any p

, either q > ˆq or q ≤ ˆq must hold. Then aﬃliate j ﬁnds either recommending

product 0 more proﬁtable regardless of his signal about product 0 or recommending a non-salient

product more proﬁtable regardless of his signal about product 0. Therefore, (α, β) = (1, 0) cannot

be an equilibrium proﬁle as p

→





. This proves that ¯p

(q, λ) >

unless q = ˆq. It also follows

that for any q ̸= ˆq, there exists an interval [

, p

(q, λ)] over which the proﬁle (α, β) = (1, 0) does

not constitute an equilibrium. This completes the proof of part (2).

Proof of Corollary 1. (1) By the proof of Proposition 3, part (1), for any λ, as p

→





, it

is strictly more proﬁtable for an aﬃliate to recommend product 0 when q = 0, and strictly more

proﬁtable to recommend a non-salient product when q = 1. By the compactness of the unit interval

[0, 1], the function λ 7→ ˆq(λ) is strictly bounded between 0 and 1. That is, there exist q and ¯q with

0 < q ≤ ¯q < 1 so that q ≤ ˆq(λ) ≤ ¯q for any λ ∈ [0, 1].

When q < q, ¯p

(q, λ) is determined by the indiﬀerence for an aﬃliate between recommending

any non-salient product for which he received a high signal and product 0 when he received a low

signal for it, whereas it is always more proﬁtable to recommend product 0 after receiving a high

signal for it for any p

. As λ increases, say, from λ

to λ

+ ϵ, recommending a non-salient

product becomes more proﬁtable: for any suﬃciently small ϵ > 0,

E[U

(i|s

(0) = l, s

(i) = h, p

= ¯p

(q, λ

), λ = λ

+ ϵ)]

> E[U

(0|s

(0) = l, s

(i) = h, p

= ¯p

(q, λ

), λ = λ

+ ϵ)].

It follows that ¯p

(q, λ

+ ϵ) < ¯p

(q, λ

When q > ¯q, ¯p

(q, λ) is determined by the indiﬀerence for an aﬃliate between recommending

any non-salient product for which he received a high signal and product 0 when he received a high

signal for it, whereas it is always more proﬁtable to recommend a non-salient after receiving a high

signal for it for any p

. As λ increases, say, from λ

to λ

+ ϵ, recommending a non-salient

product becomes more proﬁtable: for any suﬃciently small ϵ > 0,

E[U

(j|s

(0) = h, s

(i) = h, p

= ¯p

(q, λ

), λ = λ

+ ϵ)]

> E[U

(0|s

(0) = h, s

(i) = h, p

= ¯p

(q, λ

), λ = λ

+ ϵ)].

It follows that ¯p

(q, λ

+ ϵ) > ¯p

(q, λ

(2) The existence of q(λ) and ¯q(λ) follows from the same compactness argument as in the

proof of part (1). The expected utility from recommending a non-salient product is increasing

with q, whereas the expected utility from recommending the salient product remains constant as q

increases. When q < q(λ) and p

= ¯p

(q, λ), making a recommendation after receiving a low signal

about the salient product is the binding condition for an aﬃliate. Then, ¯p

(q, λ) > ¯p

(q + ϵ, λ)

for any suﬃciently small ϵ > 0. When q > ¯q(λ), making a recommendation after receiving a high

signal about the salient product is binding for an aﬃliate at p

= ¯p

(q, λ). Again, increasing q will

only increase the expected utility for an aﬃliate from recommending a non-salient product. So as

q increases to q + ϵ for some suﬃciently small ϵ > 0, ¯p

(q, λ) is weakly increasing.

Proof of Proposition 4. (1) Let n

and n

be the unique numbers of recommendations the salient

product receives in a recommendation proﬁle so that

1 ≤ n ≤ N|P r(H|0

(n)

) > p

≥ P r(H|

l, 0

(n)

)

:= min

1≤n≤N

P r(H|

l, 0

(n)

) > p

That is, n

is the threshold number of recommendations that will incentivize the consumer to ﬁrst

consider the salient product but will only purchase it when her signal is high, and n

is the threshold

number of recommendations so that the consumer will purchase the salient product regardless of

her signal. By deﬁnition, n

< n

. Depending on the number of recommendations for the salient

product the consumer sees, we consider the following three cases regarding the consumer’s best

response.

Case 1. n ≥ n

. This case leads the consumer to purchase the salient product regardless of her

signal about it. The consumer’s expected payoﬀ is

(1 − c)P r(H|0

(n)

). (15)

Case 2. n

≤ n < n

. The consumer will ﬁrst consider the salient product. She will purchase

a salient product only when her signal about it is high. Otherwise, she will continue to consider a

non-salient product. The consumer’s expected payoﬀ is

(1 − c)P r(

h|0

(n)

) · P r(H|

h, 0

(n)

) + q(1 − 2c)



1 − P r(

h|0

(n)

) · P r(H|

h, 0

(n)

)



· P r(

h|h) · P r(H|

h, h).

= (1 − c)π

· P r



H|0

(n)



+ q(1 − 2c)π



1 − π

· P r



H|0

(n)



= [1 − p

q − c(1 − 2p

q)]π

P r



H|0

(n)



+ q(1 − 2c)p

Case 3. n < n

. In this case, the consumer will only consider non-salient products. She will

only purchase it after seeing a high signal about the focal non-salient product. This is because

when she sees a low signal about it, her posterior belief about the salient product is higher than

that about the non-salient product under her consideration. After the consumer clicks on a link

to a recommended non-salient product i, her belief about the clicked non-salient product’s quality

is updated as P r(H|

h, h) =

+(1−p

)(1−π

)

or P r(H|

l, h) =

(1−π

)

(1−π

)+(1−p

)π

. The consumer’s

expected payoﬀ is:

(1 − c) · P r(

h|h) · P r(H|

h, h) + q · (1 − 2c) · (1 − P r(

h|h) · P r(H|

h, h)) · P r(

h|h) · P r(H|

h, h),

= (1 − c)p

+ q(1 − 2c)p

(1 − p

). (16)

The equality in (16) follows because

P r(

h|h) = P r(H|h)P r(

h|H) + P r(L|h)P r(

h|L) = p

+ (1 − p

)(1 − π

). (17)

Similar to the baseline model, the consumer’s expected payoﬀ attains maximum when her pos-

terior belief about the salient product is the most accurate, which must be induced by a conformity

proﬁle.

(2) Denote by p

:= P r(H|

h, h) and p

:= P r(H|

h, 0

(n)

) the consumer’s posterior belief about

a recommended non-salient product and the salient product after she clicks on a link and receives

a high signal, where n is the number of recommendations she sees about product 0.

When n ≥ n

, the consumer will purchase the salient product after one click. The aﬃliates’

aggregate expected payoﬀ is

λ + (1 − λ) · P r



H|0

(n)



. (18)

When n < n

, the aﬃliates’ aggregate expected payoﬀ is



1 + q(1 − max{p

, p

})



+ (1 − λ)



max{p

, p

} + p

q(1 − max{p

, p

})



. (19)

Comparing (18) and (19), we ﬁnd that a conformity proﬁle maximizes the aﬃliates’ aggregate

payoﬀ if and only if either

(1) 1 − p

q − (1 + q − p

q)λ > 0; or

(2) P r



H|0

(n)



1−λ

q(1 − p

) + p

+ p

q(1 − p

The ﬁrst scenario is identical to the baseline model, yielding a lower bound on p

: p

1−λ−qλ

q(1−λ)

The second scenario leads to an upper bound on p

. Note that the condition in the second scenario

is not vacuous if and only if

1−λ

q(1 − p

) + p

+ p

q(1 − p

) < 1, which gives rise to

λ <

1 − p

1 + q − p

. (20)

Note that the condition above is the identical condition for scenario 1. Therefore, we identify

the same condition that distinguishes the aﬃliates’ aggregate preference for conformity as in the

baseline model. In addition, within the case when the aﬃliates’ aggregate payoﬀ is maximized

under conformity, we identify a further reason for their preference for conformity, which is when

the consumer’s posterior belief about product 0 is suﬃciently high, the incentive for the aﬃliates

to induce the consumer to purchase product 0 after one click leads to the greatest aggregate payoﬀ

for the aﬃliates.

For parts (3) and (4), the proofs in the baseline model on the existence of a non-conformity

equilibrium and conditions for the existence of a conformity equilibrium still work. The reason

is that, for checking the proﬁtability of unilateral deviations, we only need to compare aﬃliates’

aggregate payoﬀs for special sets of parameter values (e.g., p

= 1 in the case to characterize the

condition for the existence of a conformity equilibrium). And those comparisons would not change

under the current more general setting.

Proof of Corollary 2. (1) In the model of experience goods, for every strategy proﬁle for the aﬃli-

ates, the consumer’s best response is to click on a link to a product that has the highest posterior

probability of being high quality and to purchase that product. (Because the consumer’s posterior

beliefs are identical for all of the recommended non-salient products, it is therefore unique up to

identiﬁcation of non-salient products that are recommended.) Therefore, the consumer’s expected

search length is 1, reducing q = 0. Also, the aﬃliates expect to be paid without distinguishing

being clicked only or inducing a purchase. The aﬃliates’ aggregate payoﬀ is identical to the special

case of the baseline model with λ = 1.

Therefore, to analyze the model of experience goods, it suﬃces to look at the special case with

q = 0 and λ = 1. In this scenario, the condition identiﬁed in Proposition 1 becomes vacuous,

yielding aﬃliates as a group indiﬀerent between a conformity proﬁle and non-conformity proﬁle.

(2) Part (2) follows immediately as we have shown in part (1) the equivalence of the model of

experience goods with the special model with q = 0 and λ = 1.

Online appendix I: Preliminary analysis

In this section we cover a few observations that highlight the inner workings of the model. First,

because each aﬃliate observes only a small fraction of all products, the probability that any two

aﬃliates observe (and recommend) the same non-salient product is 0 and the only product that

has positive probability of receiving multiple recommendations is the salient product (product 0).

Therefore, aﬃliates’ recommendations segment products into three categories:

(1) the salient

product—a recognisable product that can possibly receive more than one recommendation; (2)

non-salient products recommended by one aﬃliate; and (3) the remaining non-recommended non-

salient products.

Second, because only a fraction of all products is observed by any aﬃliate, if a non-salient

product does not receive a recommendation, the consumer assigns probability 1 for the product not

being observed by any aﬃliate. As a result, the posterior belief of the consumer is that a non-salient

product that is not recommended (category 3) is a high quality product is probability 1/2. Note

that because all aﬃliates observe the salient product, the same is not true for an unrecommended

salient product.

Third, for any λ < 1, an aﬃliate’s expected payoﬀs increase in the probability that, conditional

on clicking on the product he recommends, the consumer purchases the product. Because the con-

sumer is able to evaluate the product before purchasing, the probability that a consumer purchases

the product following a click is increasing in the quality of the product. As a result, as long as an

aﬃliate receives a high signal for at least one non-salient product (which happens with probability

1), it is a weakly dominated strategy for him to recommend a non-salient product for which he

received a low signal. For the same reason, in any equilibrium with weakly undominated strategies

the posterior belief of the consumer is that a non-salient product that is recommended (category

2) is of high quality with probability p

Fourth, the only undominated strategy for the consumer is to click on links to products in

the order of their posterior probabilities to be of high quality (as long as the expected utility

is higher than c), and buy a product she clicked on immediately if it is revealed to be of high

quality. Moreover, for any c > 0 the consumer will never click on a link to a product that is not

We abstract from the zero probability event in which a non-salient product receives more than one recommen-

dation. Accommodating that possibility adds some special cases (all zero probability) to the analysis but doesn’t

introduce any new insights.

recommended by any aﬃliate.

Online appendix II: Further characterizations of equilibria

First, it is straightforward to verify that non-conformity always leads to an equilibrium.

Proposition OA.1. There always exists a pure-strategy equilibrium in which none of the aﬃliates

ever recommend the salient product regardless of their signals about it and the consumer proceeds

by only searching among non-salient products that are recommended.

Next, let N > 2 be the number of aﬃliates whose recommendations the consumer will observe.

For any q ∈ [0, 1] and λ ∈ [0, 1], let p

(q, λ) be identiﬁed by Proposition 3. That is, p

(q, λ) is the

smallest value so that the strategy proﬁle with aﬃliates recommending according to (α, β) = (1, 0)

and the consumer searching in a posterior-belief-descending order can be sustained for any p

∈

(q, λ), 1].

Proposition OA.2.

(1) For any p

> p

(q, λ), the following proﬁle is supported as a mixed-strategy equilibrium: the

aﬃliates play according to (α(p

), 0) for some uniquely determined α(p

) ∈ (0, 1), and the

consumer proceeds her search in a posterior-belief-descending order.

(2) For any p

> p

(q, λ), the following proﬁle is supported as a mixed-strategy equilibrium: the

aﬃliates play according to (1, β(p

)) for some uniquely determined β(p

) ∈ (0, 1), and the

consumer proceeds her search in a posterior-belief-descending order.

Proof. (1) We ﬁrst consider possible mix-strategy equilibria of the form (α, 0) with 0 < α < 1—

every aﬃliate recommends the salient product with probability α after receiving a high signal about

it and recommends a non-salient product after receiving a low signal about product 0, and the

consumer proceeds with her search in a posterior-belief-decreasing order (among the recommended

non-salient products, since the consumer’s posterior belief about them are equal, when she decides

to consider non-salient products, she will randomly pick one with equal probability).

Suppose that aﬃliate i receives a high signal about product 0: s

(0) = h. His estimate of the

probability that among the other N − 1 aﬃliates s of them also receive high signals about product

0 is

P r



, l

N−1−s

)|s

(0) = h





N − 1



s+1

(1 − p

)

N−1−s

+ (1 − p

)

s+1

N−1−k

. (21)

Hence, after a high signal about product 0, aﬃliate i’s expectation that product 0 will receive k

recommendations from other aﬃliates is

(k)

N−1

s=k





P r



, l

N−1−s

)|s

(0) = h



(1 − α)

s−k

. (22)

For consumer’s posterior belief about product 0, conditional on product 0 having high quality,

the probability that the consumer will see k recommendations of product 0 is

P r



(k)



= α

N−k

i=0



N − i



N − i



k+i

(1 − p

)

N−k−i

(1 − α)

. (23)

We can also derive the probability P r(0

(k)

|L) that the consumer will see k recommendations of

product 0 conditional on product 0 having low quality. Then the consumer’s posterior about

product 0 after seeing k recommendations is

P r



H|0

(k)



P r



(k)



P r



(k)



+ P r



(k)



N−k

i=0



N−i



N−i



k+i

(1 − p

)

N−k−i

(1 − α)

N−k

i=0



N−i



N−i



k+i

(1 − p

)

N−k−i

+ (1 − p

)

k+i

N−k−i

](1 − α)

. (24)

Similar to the pure-strategy case where (α, β) = (1, 0), we can ﬁnd a unique k

(α) such that product

0 needs to receive at least k

(α) recommendations for the consumer to consider ﬁrst. Since the

consumer’s search lasts at most two steps, she will not consider product 0 when more than one

non-salient products receive recommendations and she did not start the search with product 0.

In the proposed mixed-strategy equilibrium with 0 < α < 1, after seeing a high signal about

product 0, aﬃliate i must be indiﬀerent between recommending product 0 and non-salient product

j for which he receives a high signal. The indiﬀerence condition is

E[U

(0|s

(0) = h, p

, α)] = E[U

(j|s

(0) = h, s

(j) = h, p

, α)] (25)

⇔

N−1

k=k

(α)−1

λ + (1 − λ)P r



H|0

(k+1)



k + 1

(k)

(α)−2

k=0

Γ(λ, q)E

(k)

(26)

where as before

Γ(λ, q) = λ



N − k

(1 − p

N − k − 1



+ (1 − λ)



N − k

(1 − p

N − k − 1



. (27)

To conﬁrm the existence of a mixed-strategy equilibrium of the form (α, 0), it suﬃces to show that

Eq. (26) has a solution in α ∈ (0, 1) for any given set of parameters λ, q and N, and when p

suﬃciently high.

When p

> ˆp

(q, λ) and when all other aﬃliates deploy the strategy (α, β) = (1, 0), it is

strictly more proﬁtable for aﬃliate i to also play according to (α, β) = (1, 0), based on the previous

analysis on the pure-strategy equilibrium (α, β) = (1, 0). Similarly, when p

> ˆp

(q, λ) and when

all other aﬃliates deploy the strategy (α, β) = (0, 0), it is strictly more proﬁtable for aﬃliate i to

also play according to (α, β) = (0, 0) from the previous analysis on the pure-strategy equilibrium

(α, β) = (0, 0). Therefore, there exists some α(p

, q, λ) ∈ (0, 1) that equalizes an aﬃliate’s expected

utility from recommending product 0 and a non-salient product after receiving high signals about

both when all the other aﬃliates play according to the mixed strategy (α(p

, q, λ), 0).

Lastly, when aﬃliate i receives a low signal about product 0, and when all the other aﬃliates

play according to the mixed strategy (α(p

, q, λ), 0), it is strictly more proﬁtable for aﬃliate i to

recommend a non-salient product at α = α(p

, q, λ) when p

> ˆp

(q, λ). Therefore, the mixed-

strategy proﬁle of the form (α(p

, q, λ), 0) gives rise to an equilibrium when the consumer searches

in a posterior-belief-descending order.

(2) Consider the mix-strategy proﬁle of the form (1, β) with 0 < β < 1. Note that after a high

signal about product 0, aﬃliate i’s expectation that product 0 will receive k recommendations from

other aﬃliates is

(k)

s=0



N − 1 − s

k − s



P r



, l

N−1−s

)|s

(0) = h



k−s

(1 − β)

N−1−k

. (28)

Conditional on product 0 having high quality, the probability that the consumer will see k recom-

mendations of product 0 is

P r



(k)



= (1 − β)

N−k

i=0





N − i

k − i



(1 − p

)

N−i

k−i

. (29)

We can similarly derive the probability P r



(k)



that the consumer will see k recommendations

of product 0 conditional on product 0 having low quality. Then the consumer’s posterior about

product 0 after seeing k recommendations is

P r



H|0

(k)



P r



(k)



P r



(k)



+ P r



(k)



i=0





N−i

k−i



(1 − p

)

N−i

k−i

i=0





N−i

k−i



(1 − p

)

N−i

+ (1 − p

)

N−i

]β

k−i

. (30)

We can ﬁnd unique k

(β) < k

′

(β) such that product 0 needs to receive at least k

(β) and at most

′

(β) recommendations for the consumer to consider ﬁrst.

After seeing a low signal about product 0, aﬃliate i is necessarily indiﬀerent between recom-

mending product 0 and a non-salient product j for which he receives a high signal. The indiﬀerence

condition is

E[U

(0|s

(0) = l, p

, β)] = E[U

(j|s

(0) = l, s

(j) = h, p

, β)] (31)

⇔

′

(β)−1

k=k

(β)−1

λ + (1 − λ)P r



H|0

(k+1)



k + 1

(k)

k<k

(β)−1 or k≥k

′

(β)

Γ(λ, q)E

(k)

(32)

where as before

Γ(λ, q) = λ



N − k

(1 − p

N − k − 1



+ (1 − λ)



N − k

(1 − p

N − k − 1



. (33)

To conﬁrm the existence of a mixed-strategy equilibrium of the form (1, β), it suﬃces to show that

Eq. (32) has a solution in β ∈ (0, 1) for any given set of parameters λ and q, and when p

suﬃciently high.

When all the other aﬃliates play according to the strategy (α, β) = (1, 1), when p

is suﬃciently

high, it is strictly more proﬁtable for aﬃliate i to also play according to (α, β) = (1, 1). Then

there exists some β(p

, q, λ) ∈ (0, 1) that equalizes aﬃliate i’s expected utility from recommending

product 0 after a low signal about it and a non-salient product for which he receives a high signal,

when all other aﬃliates also play according to (α, β) = (1, β(p

, q, λ)):

E[U

(0|s

(0) = l, β = β(p

, q, λ))] = E[U

(j|s

(0) = l, s

(j) = h, β = β(p

, q, λ))]. (34)

This also shows that when aﬃliate i receives a high signal about product 0, it is strictly more

proﬁtable for him to recommend product 0. This completes the proof of the existence of a mixed-

strategy equilibrium in which aﬃliates play according to (α, β) = (1, β(p

, q, λ)) and the consumer

searches in a posterior-belief-descending order.