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QUANTITY VERSUS QUALITY: AN EXPERIMENT ON THE EFFECT OF
INCENTIVES ON INFORMATION SHARING
JONATHAN LAFKY AND ALISTAIR J. WILSON
A BSTRACT. Public information sharing has become increasingly important in helping individuals make better, more informed choices. Our project uses a novel theoretical framework and laboratory experiments to analyze three simple, commonly used incentive schemes against an unincentivized baseline. Each incentive scheme has qualitatively different theoretical predictions for behavior and efficiency, while our laboratory experiments examine the degree to which these differences manifest themselves, and the best-case theory’s robustness to human behavior. Our findings indicate the possibility for substantial efficiency gains by introducing incentives that reward the provision of public information, even where those incentives drive a wedge between those providing and making use of information. In particular, our results point to a misaligned incentive commonly found in the field, sales commissions, as being a robust institution to stimulate the exchange of information.
Information is profitably shared by friends, colleagues and even strangers. A friend may volun- teer their positive experience with a new car model, while the stranger on the street might point us further down the road to a better coffee shop. Placing faith in others’ opinions allows us to use their experiences to make better choices for ourselves. This can lead us to pay more for a recommended car than a competing model, or walk slightly farther for a better espresso. Consumers have long relied on newspapers and periodicals to review new products for over a century: from books and plays, to consumer electronics and movies. More introspectively, academic journal editors have long relied upon disinterested peer reviews to advise them on publication decisions. In the above examples, and in many similar settings, decision makers benefit when informa- tion is shared openly. In this paper, we examine the potential for economic incentives to increase information sharing. In particular, we look at three common incentive schemes, each of which produces tradeoffs over the intensive and extensive information margins, as well as the distribu- tion of the gains from information sharing. In each incentive environment we examine tradeoffs between quality (the intensive margin) and quantity (the extensive) in information sharing, where we measure quantity as the likelihood that any advice is shared, and quality as the content of that advice.^1
Date: February, 2016. Lafky: Lafayette College, 110 Simon Center, Easton, PA ; lafkyj@lafayette.edu. Wilson: University of Pittsburgh, Department of Economics, 230 Bouquet Street, Pittsburgh, PA; alistair@pitt.edu. Our thanks to the following: John Asker, John Duffy, Matthew Embrey, Emanuel Vespa, Lise Vesterlund, Stephanie Wang, and audiences at the ESA, SEA, George Mason, and Lafayette. Any mistakes within are obviously not attributable to anyone but ourselves. (^1) In some sense quantity and quality are interchangeable, as we could simply measure the total amount of infor-
mation transmitted. Practically speaking, however, there are important distinctions between the the two measures, especially from the perspective of designers of ratings systems. This distinction is especially important for field data, where it is generally easy to observe the frequency with which ratings are given, but difficult or impossible to learn their accuracy.
While theory can make normative predictions on the effect of the distorting incentives—and indeed, we provide such an analysis—to do so typically requires strong equilibrium selection as- sumptions. An inherent multiplicity of prediction is a generic feature of cheap-talk games, and so comparative-static predictions from the best-case equilibrium (or any other consistent selection) may have little predictive power. Indeed, just the presence of a commonly known incentive could be enough to plausibly affect selection. To address this issue we examine an experiment that sets out to answer a number questions that theory or field data will struggle to answer: How effectively can we increase the provision of information by introducing incentives? Do the comparative-static predictions from the best-case equilibrium have predictive power in our data? Do incentives distort the information provided or are honesty norms too strong? How do those receiving information respond to the presence of different incentives? What are the impacts on sales and efficiency? The rich theoretical framework we set out mirrors a variety of information-sharing settings, with an informed sender reluctant to communicate due to a personal cost of providing information, but otherwise with interests that are fully aligned with an uninformed consumer. The best-case outcome in this environment exhibits inefficient under-provision, where the sender too often offers no advice. Though high-quality advice is sent when the cost of communicating is small, low rates of provision lead to an inefficient outcome. To this baseline setting we compare three possible incentive environments, each with their own advantages and disadvantages. The first incentive, which we call Receiver, is the most obvious to economists: a monetary transfer from the consumer making use of the information to the party providing it. Maintaining the alignment of interests, this institution provides a transfer conditional on both the provision and acquisition of information. Examples of this incentive include: printed reviews in newspapers, paying referees, and paid subscriptions for access to rating aggregates (for example, Zagat’s or Angie’s List). Though receiver-to-sender transfers can help increase quantity while maintaining quality, there are potential issues. The first is distributional: As the transfer becomes larger, more of the gains from information transmission are shifted to the party providing information. In fact, for large enough payments, final consumers can be made worse off than with no incentive for infor- mation sharing. The second issue is equilibrium selection. Babbling equilibria with no information sharing will always exist in this setting, representing the absence of any information transmission.^2 As the size of the incentive payment increases, coordinating on an efficient informative equilibria becomes more-and-more risky for those acquiring information. Our remaining two incentives look to parties other than the final consumer to subsidize infor- mation transfer. The second incentive, labeled Vendor, implements a payment from a marketplace that sells a variety of competing products. The Vendor incentive provides a payment for each sale made, regardless of the chosen product chosen, mirroring a sales-commission incentive. The theo- retical effect in the best-case equilibrium is to trade off alignment of interest between those sharing information, and therefore quality of the information transmitted, in exchange for greater provi- sion. Sales-contingent incentives are commonplace, with examples such as: salespeople at multi- product stores or brokers offering advice over different investments (explicit sales commissions); servers providing advice on the dessert menu (implicit through a larger tip); and product-review
(^2) For an example of such selection in the field, take Google Answers, a website where those seeking information
directly compensated those providing it. The website was eventually closed after the community using it became too small.
outcomes of our four institutions, due to the transfers receivers must make to acquire this informa- tion. We instead find that implementing a sales-commission incentive that trades off alignment-of- interest with the informed party in exchange for greater provision leads to superior outcomes for recipients. After analyzing our experimental results, we extend our analysis through two counterfactuals that further bolster our results that sales-commission incentives offer the best outcomes. The first exercise extrapolates our findings across a broader range of parameters by varying the distribution of consumers’ outside options. We show that sales-based incentives to those providing advice produce higher final-consumer welfare and increased total sales across a broad range of values for the expected outside options, suggesting our results are not driven by our particular choice of parametrization. More specifically, we show that specific producers interested in the sales of their own products do better in the long run (that is, where the incentive’s presence is commonly known) with the Vendor incentive than the Producer. This motivates our second counterfactual, which uses our data to examine the extent to which marketplaces and producers might profit in the short-run by secretly introducing misaligned incentives. The results indicate that substantial short-run profits are available to manufacturers who surreptitiously offer those providing advice an incentive to gin-up sales. In contrast, these short-run gains are much smaller when introduced into the already partially misaligned Vendor environment. Taken together, the two counterfactuals suggest that sales-contingent incentives at the mar- ketplace level are the more-efficient stable institution. In comparison to the other environments the sales incentives generate long-run gains to final consumers, marketplaces and to producers with existing customer bases. Moreover, while firms contemplating the covert introduction of Producer-style marketing schemes into a Vendor environment will suffer long-run losses from re- duced credulity, the short-run gains are much smaller than they would be if interests were fully aligned, per the Receiver case. Environments with sales commission therefore provide a measure of inoculation to the introduction of incentives that might poison the well.
1.1. Related Literature. The theoretical starting point for the information transmission literature is Crawford and Sobel (1982), which describes the impossibility of full revelation with cheap talk when senders of information have misaligned preferences with receivers. Where the senders have state-dependent preferences, the upper bound for information revelation is shown to be decreasing in the size of the misalignment. Our aligned-incentive institutions have state-dependent preferences for senders with zero bias term, and with a larger message space full revelation would be possible. However, our misaligned-incentives bear more resemblance to the state-independent preferences with multiple dimensions in Chakraborty and Harbaugh (2010), where the sender is misaligned in one or many of these dimensions. In our setting these two dimensions are the particular product, and the receiver’s WTB. Our environment has costs for both sending and acquiring messages. 4 However, these costs are not message specific, and the cost is incurred if any message is sent or received. Because the send cost does not vary with the sender’s type, our paper is more related to the cheap talk literature than to the costly signaling literature.
(^4) A related paper with costs to both senders and receivers is Dewatripont and Tirole (2005), though there costs
vary over the precision of articulation or interpretation of the message. See also Dessein and Santos (2006); Calvó- Armengol, de Martí, and Prat (forthcoming) for models of endogenous communication with costs.
Several papers have examined incentives for communication from the perspective of online ratings. Chen, Harper, Konstan, and Li (2010) use social comparison between users of a movie rat- ing website to increases rating provision, while Wang (2010) argues that increased social identity increases provision. There is also evidence that ratings given in the absence of explicit incen- tives may be subject to systematic biases as in Hu, Zhang, and Pavlou (2009) and Lafky (2014), which demonstrate the tendency for raters to over-report positive or negative experiences, relative to moderate outcomes. 5 There is also some evidence for biases due to self-selection, as in Li and Hitt (2008), where consumers who are predisposed towards a product are more likely to rate early in the product’s lifespan, leading to artificially positive ratings. A body of work has experimentally examined tensions between agents in the Crawford and So- bel environment. 6 The main experimental finding is that subjects over-communicate relative to the- ory: senders tell the truth more often than predicted, and receivers infer honesty too much, though with a large heterogeneity explained via level-k thinking. In a setting closer to our own, Wilson (2014) examines the behavior of subjects in aligned-interest groups with similar two-sided costs. He finds subjects under-respond to the costs of sending messages, and overpay to acquire informa- tion, relative to the gains obtained. In contrast, our own paper examines institutional changes that influence the cost of sending and receiving messages, and the extent to which senders are aligned with receivers. Taking away the costs of communication, and independent of our own work, Chung and Harbaugh (2012) examine the extent to which observed play matches the equilibrium predic- tion in a similarly structured sender-receiver environment. Receivers face a choice between two products and an outside option. They find that messages are persuasive, even in those environments where theory predicts they should not be, matching a result we find in our misaligned treatments.^7
2. T HEORETICAL F RAMEWORK
In this section we introduce our formal framework. We then introduce the four environments we will analyze, and provide an informal discussion of the most-informative equilibria, where readers interested in more formal constructions are referred to the appendix. After the informal discussion of equilibria for general parameters, we move on to the specifics in the next section, where we introduce the experimental parametrization, and indicate the most-informative equilib- rium outcomes. To begin constructing our framework we first describe the uninformed consumers problem: A representative consumer R (the receiver, he) faces a choice between two initially symmetric, non- divisible products, product A or product B. The consumer has a unit demand for either product, but can also choose to purchase neither, and consume an outside option with a privately known value ! 2 R, drawn according to a CDF H. If R chooses a product Z 2 {A, B}, he forgoes his outside option, and receives a product with some random quality/utility level z 2 ⇥ = {✓ 1 ,... , ✓ (^) N } ⇢ R. We denote the outside-option choice as R (as in they choose themselves), so the overall choice set
(^5) Also see Bolton, Greiner, and Ockenfels (2013) with respect to managing the distortive effects of reciprocity when
ratings are two-way. (^6) See Dickhaut, McCabe, and Mukherji (1995), Cai and Wang (2006), Wang, Spezio, and Camerer (2010). For
extensions to multiple senders or receivers see Lai, Lim, and Wang (2011); Vespa and Wilson (2014) and Battaglini and Makarov (2014). (^7) See also Charness and Garoupa (2000) which examines the extent to which reputation affects revelation, where
senders have a state-independent preference to induce sales.
Against these two extremes (full frictionless exchange and no information transfer) we will consider equilibrium predictions and experimental behavior where information transmission be- tween the consumers has frictions: where the provision of information incurs private costs to the sender; where the language available to communicate information is limited; and where acquisition of provided information to the receiver is costly. Given sender provision costs, a second-best outcome emerges in equilibrium in which con- sumers, merchants, and the manufacturers of specific products benefit from greater provision. Our analysis will consider three plausible institutions for increasing provision, and examine equilibrium predictions and experimental behavior in each regime. Under a particular institution , we will ex- amine the expected gross outcome for receivers, W ( ) = Ew (^) R (Z; ), normalized to indicate the efficiency of information transfer as:
⌥( ) =
W ( ) W
W W
That is, we measure efficiency as the gain in W ( ) relative to the individually rational, no- communication lower bound W , as a fraction of the the maximal information exchange possible in a frictionless setting, (W W ). The full sender-receiver game’s timing is as follows: (i) Nature draws a state of the world ( A^ , B^ , c S^ , !) where A^ and B^ are iid draws from a set of lotteries ⇢ ⇥; c S^2 R is a cost of provision drawn independently from a CDF G; and! 2 H ⇢ R is a reservation, drawn independently from CDF H. (ii) S observes her send cost c S^ , and obtains a single draw x from X^ , where the initial product X 2 {A, B} is selected with equal probability. Given the signal (X, x), her choice is a rating/message m 2 M [ {m (^) ; }, where M is a set of meaningful ratings, and m (^) ; is the empty message, choosing not to provide. Choosing any m 2 M incurs the cost c S^ , while choosing not to provide, m = m (^) ; , is free. (iii) R observes whether there was a provided rating, learning either that {m 2 M} or that {m = m (^) ; } has occurred. If {m 2 M} he first chooses whether or not to acquire the infor- mation, ⇢ 2 {View, Not}, incurring a fixed cost c R^ > 0 only when he views.^10 (iv) R observes his private outside option !, and the precise rating m 2 M if viewing. He then makes a choice Z 2 {A, B, R}, with a realization z from Z^ if a product is chosen, and! if he selects the reservation.^11
Completing the specification of the game over the action choices (m, ⇢, Z), S and R’s preferences are modeled through the net utility functions
u (^) S (m, ⇢, Z) = x + ↵ · w (^) R (Z; !) c S^ · 1 {m 6 = m (^) ; } + (^) S (m, ⇢, Z) · T, u (^) R (Z, ⇢, m) = w (^) R (Z; !) c R^ · 1 {⇢ = View, m 6 = m (^) ; } (^) R (m, Z, ⇢) · t,
where ↵ > 0 is a preference parameter reflecting a prosocial incentive to help receivers make better product choices. 12 The institution is reflected by a conditional transfer T > 0 to (t > 0 from) the
(^10) The cost c R (^) can be thought of as a small nuisance cost of viewing a rating. Intuitively, this is the small amount
of time and effort it takes to read and comprehend a message. (^11) We assume that the realization of! happens after rating viewing for tractability. The first-order effect from
alternating the order is to reduce viewing behavior for those R-types with high reservations. (^12) The sender having a lexicographic preference over the receiver outcome, subordinate to her own outcome, would
also suffice for our needs. The required assumption is simply that conditional on sending a non-empty message, the sender and listening receiver are strongly aligned in interest over the choice Z.
sender (receiver), conditioned on the specific events indicated through (^) S (m, ⇢, Z) 2 { 0 , 1 } (and
R (m,^ ⇢, Z)^2 {^0 ,^1 }). The transfer conditions can therefore respond to any of the action choices made in the game, where our paper will focus on four simple variations. A pure strategy for the sender is a rating choice μ : {A, B} ⇥ ⇥ ⇥ R! M [ {m (^) ; }, a decision on the rating to send given the signal (X, x) and provision cost c S^. The strategy for the receiver is the tuple (⇢, {⇣ (^) m }m 2 M , ⇣ (^) M , ⇣ (^) ; ): a listening decision ⇢ 2 {View, Not}, and a product choice ⇣ (^) I : H! {A, B} [ {R} for every possible information set, I 2
S
k 2 M {m^ =^ k}^ [^ {m^2 M}^ [ {m = m (^) ; }. 13 The relevant choices for R are: i) viewing the provided rating m, and responding with ⇣ (^) m ; ii) knowing that a rating was provided, m 2 M, but not viewing it, with a response ⇣ (^) M ; and iii) knowing that no rating was provided, and responding with ⇣ (^) ;. Beliefs at every information set I for S and R are given by (^) S (I) and (^) R (I), which are conditional distributions over the entire state ( A^ , B^ , c S^ , !). Our solution concept will be Perfect Bayesian equilibrium (PBE), < μ?^ , ⇢?^ , ⇣?^ ; ? S , ? R >, where we focus on illustrating the most-informative and least-informative PBEs under two symme- try restrictions. The first restriction is that we restrict attention to symmetric messaging strategies over the two products, so that there exist complementary messages, and similar quality experiences (the specific draw x) lead to similar ratings, regardless of the precise sampled product identity (X = A or X = B). The second restriction is that when agents are indifferent over Z 2 {A, B}, any resulting ties are broken by an equal randomization between them, where all other strategy components are pure. The reasoning behind these restrictions is to focus on symmetry between the two products being broken by ratings ex post, and not through an ex ante coordination on a particular product.^14 Given the description of the environment, we now describe the four environments we will compare. We first introduce the specific transfer rules , and then provide a qualitative description of the most-informative equilibrium. The environments we will study are:
Baseline. No conditional transfers, so S^ (m, ⇢, Z) = R^ (m, ⇢, Z) = 0 for all possible action choices. So long as c R^ is not too large and there are senders with low enough provisions costs, in- formation transfer is possible in equilibrium. 15 However, because the provision cost c S^ is privately incurred by senders, there may be draws for which senders do not provide a rating, and select m (^) ; instead. The main tension in the Baseline environment is on provision, where rational senders will under-provide information relative to the benefit receivers derive. 16 In an environment with transferable utility where ↵ is small, a Pareto improvement will be possible at costs c S^ > 0 , where receivers pay for rating provision, which leads us to the next institution.
Receiver Transfer. One simple policy to ameliorate the provision failure in the Baseline is a trans- fer from the receiver to the sender. Should a non-empty rating be provided, each receiver viewing
(^13) We allow for receivers to randomize over the two products A and B to maintain symmetry in the case where no
information is revealed. However the focus of the paper is on how ratings provided by S allow us to break symmetry. (^14) Moreover, in our experimental environment, we will explicitly prohibit any such coordination by randomly rela-
beling A and B between the sender and receiver. (^15) A sufficient condition for the second part is that G(0) > 0 , so a positive fraction of senders have no cost or enjoy
sending. In the experiment subjects do receive negative cost draws for sending, with the interpretation being that these senders (net any costs) enjoy sending information to others. (^16) In informative equilibria, the decision to provide or not can be characterized by a signal-specific cutoff
c?^ (⌫ (^) X (x); ) where the sender provides a rating in m 2 M for all c S^ c?^ (⌫ (^) X (x); ). The theoretical appen- dix provides additional details.
Similar to the receiver transfer, this environment has the effect of reducing sender’s provision costs in informative equilibria, and therefore increasing the quantity of information. However, if the conditional transfer T is large in relation to the altruism term ↵, the transfer has a negative effect on alignment of interest between S and R: they are now only partially aligned. Senders derive a benefit from receivers buying a product, regardless of their particular reservation !, though they are still aligned with the receiver over which product A or B should be chosen. For ↵ small, the most-informative equilibria restrict senders to providing just two effective ratings, with the ordinal interpretations “A B” and “B A.” The statement that A B tells the receiver that the sender’s signal is in {(X, x) |E [w (^) R (A) |x] > E [w (^) R (B) |x]}.^19 Whether receivers are better off here than in the most-informative equilibria in the Baseline and Receiver environments depends on the specifics. On the one hand, the provision of informative ratings increases, and receivers are not paying for the provision subsidy. On the other hand, the amount of information conveyed with each rating is more restricted. Similarly, providing such a transfer may or may not help increase product sales for the vendor player. From the vendor’s perspective, this conditional transfer can be sensible both as a short-run marketing response to the Baseline setting, and in the long run. If a large mass of final consumers have reservations just above ✓¯, such a policy will be very effective. Every provided rating is predicted to have a positive influence on sales. A rating with the content “A B” leads to expected qualities satisfying ⌫ (^) A (A B) > ✓¯ > ⌫ (^) B (A B). As such, every provided and viewed rating is predicted to increase WTB to ⌫ (^) A (A B) from ✓¯. In comparison, in the aligned-interest setting, many provided ratings will simply say that a particular product is below average, having no effect on total sales. The sales benefits from this type of incentive have a limit though, and in environments where the large mass of receivers have reservations far above ⌫ (^) A (A B) (or for that matter below ✓¯), a sales-incentive will be ineffective at generating increased vendor revenue. In the Baseline and Receiver cases there are equilibria where senders with very good product experiences can influence high-reservation receivers. In Vendor though, the lack of alignment between S and R over WTB limits the extent to which a high-reservation receivers can be persuaded to purchase—no receiver with! > ⌫ (^) A (A B) will ever make a purchase in equilibrium. Similarly, for any receivers with ! < ✓¯ , sales-conditioned incentives are ineffective marketing tools for vendors, as these receivers would have purchased a product even in the absence of any provided information.
Producer Transfer. Our final institution considers a transfer to senders provided by the specific producer X 2 {A, B} with which the sender has product experience (through a unique coupon in product X’s packaging, say). Here we consider the transfer T to the sender only if the receiver purchases the specific product X,
S (^) (m, ⇢, Z) =
1 if Z = X, 0 otherwise,
where we again set R^ = 0 in all situations, as the transfer is paid for by the producer X. We could strengthen the condition and require that the rating be viewed as well, however the equilibrium outcome would be essentially the same.
(^19) If ↵ is very large and T small, more-informative equilibria exist. In cases where T is not large enough for senders
to provide at every c s^ (and ↵ is not negligibly small) changes in the probability of providing a rating given the signal x must also be incorporated. This effect is very small under our experimental parametrization at the equilibrium, and so we will not focus on it in our discussion of the theory.
Whenever the transfer T is large relative to ↵, the only equilibria are babbling and involve zero-information transfer (where the appendix provides a sufficient condition). If receivers view and alter their purchasing decisions based on ratings (either substituting between products, or in- creasing their WTB) then senders have a signal-independent incentive to choose the rating that increases the likelihood of an X sale. As such, in any equilibrium, ratings convey no meaning- ful information about X, and receivers choose not to view as c R^ > 0. Though such incentives may generate a significant sales boost to producers in the short-run if introduced without receiver’s knowledge, the effect is to poison the well in the long run as receivers learn of their presence. Any transfers made from the producer X to the sender that are linked to sales are therefore predicted to be ineffective in equilibrium. More developed and detailed constructions for the theory, and a formal description of the equi- librium concept used to generate the theoretic predictions are provided in the appendix. We now illustrate the specifics through our experimental parametrization.
- E XPERIMENTAL D ESIGN
3.1. Experimental Procedures. We utilize a between-subject experimental design over four treat- ment environments, paralleling a Baseline environment with no transfers, and the three conditional transfers to senders described above: a Receiver transfer conditioned on a viewed rating; a Vendor transfer conditioned on a viewed rating and a sale; and a Producer transfer from producer X, con- ditioned on a sale of product X. In each treatment, subjects participate in 30 rounds of the fixed environment, with random anonymous matching. We now detail the chosen parametrization for the experiment.
Determining the state. The primary uncertainties in the model are the quality distributions A^ and B^. The experiment’s proxy for these distributions are two urns, Urn A and Urn B. Each urn is filled with two balls labeled with an integer between 1 and 100, so the possible set of realizations for each ball is ⇥ = { 1 ,... , 100 }. In every round t and for every sender i, the two urns are independently filled via the following procedure: i) An initial ball ✓ 1 is placed in the urn, where each integer value from 1 to 100 is equally likely; ii) with probability 1 / 2 , the second ball ✓ 2 is another independent uniform draw from 1 to 100, and with probability 1 / 2 the second ball is a copy of the first ball, so ✓ 2 = ✓ 1. An urn X is completely determined by the two balls in the urn, ✓ X 1 and ✓ 2 X , and choosing urn A or B is equivalent to choosing the lotteries 12 · ✓ A 1 12 · ✓ A 2 or 12 · ✓ 1 B 12 · ✓ 2 B , respectively. The set of all possible urns, =
(^) r 2 ⇥
9 ✓, ✓ 0 2 ⇥ s.t. (^) r = 1 2 ·^ ✓^ ^
1 2 ·^ ✓^
(^0) , has
5,050 possible lotteries, where the prior probability p (^) r of the urn being the lottery (^) r = 12 · ✓ 12 · ✓ 0 is given by
p (^) r =
(^1) / 10 , 000 if ✓ 6 = ✓ 0 , (^101) / 20 , 000 if ✓ = ✓ 0.
The particular balls in an urn are correlated—an urn with two identical balls is as likely as an urn with two independent balls—and the expected subsequent draw given a previous draw x is ⌫ (^) X (x) = 3 / 4 · x + 1 / 4 · ✓¯. Half the time the new draw is the same exact ball drawn previously (value x), a quarter of the time the new draw is a copy of the previously drawn ball (value x again), and a quarter of the time the new draw is an unrelated ball (with expectation ✓¯). The other components of the state are the sending cost c S^ and the reservation !, which are determined as follows: the cost c S^ is an iid draw from G = { $0. 49 ,... , $2. 50 }, where the probability of each cost level is linearly decreasing to zero at c S^ = $2. 50 ; the reservation value
$0. 10 ⇥ !jt , respectively, so receivers get $0.10 multiplied by the value of the final ball selected. The total payoff from the receiver phase is subsequently
u (^) R (m (^) it , ⇢jt , Zjt ) = $0. 10 ⇥w (^) R (Z (^) jt ) $0. 05 ⇥ 1 {⇢jt = View, m (^) it 6 = m (^) ; } $0. 50 ⇥ R^ (m (^) it , ⇢jt , Zjt ).
Last 15 rounds. The second half of each session has a similar structure to the above. However, after the first 15 rounds, subject decisions are collected through a strategy method to collect a richer set of information.^23 Instead of showing subjects the send cost c Sit and choosing whether or not they wish to send the provisional rating mˆ (^) it , they now specify a cutoff cost C (^) it 2 G below which they would be willing to send. Similarly, receivers are not informed of their specific reservation draw !jt , and they instead specify a reservation cutoff ⌦ (^) jt 2 H (the certainty equivalent) below which they would choose the risky draw z (^) jt , and above which they would choose the realized reservation !jt. Data from interactions in rounds 1–15 are therefore given by
Ait , Bit , c Sit , !jt
⇣ ,^ (X^ it^ ,^ mˆ^ it^ , m^ it^ )^ , ⇢ (^) jt , I (^) jt , Zˆ (^) jt , Zjt
⌘E
; while data from rounds 16–30 are given by
Ait , Bit , c Sit , !jt
X (^) it , mˆ (^) it , C (^) it
⇢ (^) jt , I (^) jt , Zˆ (^) jt , ⌦ (^) jt
⌘E
.^24
3.2. Equilibrium Predictions. Given the parameters chosen for the model above, Table 1 pro- vides predictions for the main economic variables in the most informative PBE (under the sym- metry restrictions) in each treatment. These predictions assume risk neutrality with respect to the final monetary gambles, where a comparable table in the appendix presents predictions under a risk-averse formulation. For both the Baseline and Receiver treatments, the most-informative equilibrium involves send- ing a single rating (^1) X for all senders types (X, x) with x 50 and with the ratings (^2) X – (^5) X selected after the signals x in 51–61, 62–73, 74–86, and 87–100, respectively. As such, both treatments utilize all five ratings for both products, and all ten ratings are sent with positive probability.^25 The first-order difference in behavior across the Baseline and Receiver treatments is the rate at which senders provide information, Pr
μ?^
X, x, c S^
2 M , given in the Rating Provision row in Table
- In the Baseline, information is provided approximately a third of the time, while in the Re- ceiver case, provision is almost complete. 26 The extent to which decision-relevant information is exchanged is measured by ⌥ which is given in the Info. Efficiency row. This measure examines
(^23) For a survey of papers examining (and for the most part supporting) the strategy method relative to direct-response
see Brandts and Charness (2011). (^24) The corresponding realized decisions are given by: m (^) it = mˆ (^) it if c S it ^ C^ it^ and otherwise^ mit^ =^ m;^ ; and Z (^) jt = Zˆ (^) jt if! (^) jt < ⌦ (^) jt and Z (^) jt = R otherwise, (^25) Less efficient equilibria exist where, for instance, the messages 3, 4 and 5 imply products that are better than
average. With just one sender and homogenous risk preferences, messages implying a below-average product are strategically identical, so though ratings of one and two can be sent for 1–25 and 26–50, respectively, there is no incentive for this split as each rating carries a similar interpretation of “do not buy.” However, with more than one sender, ratings distinguishing between levels of below-average quality may help to aggregate information on the urn’s composition. (^26) In informative equilibria, fixing the signal (X, x), the same rating μ? (^) (X, x, c S (^) ) 2 M is sent whenever the cost
of provision c S^ is less than or equal to a cutoff c?^ (⌫ (^) X (x)), and for all send costs greater than this the empty rating m; is chosen. So long as ↵ > 0 , the cutoff c?^ (⌫ (^) X (x)) is increasing in
⌫ (^) X
✓ SX
✓¯
. Given the parametrization, and selection of the most-informative symmetric PBE, this leads to a U-shaped effect on provision conditional on the drawn signal x. The effect is strongest in the Baseline, and completely absent in the Producer treatment.
TABLE 1. Most-Informative Risk-Neutral Equilibrium Predictions
Baseline (B) Receiver (R) Vendor (V) Producer (P) Comp. Static Distinct Ratings 10 10 2 0/Babbling Rating Provision 0.346 0.980 0.934 0.304 R V B P Info. Efficiency, ⌥ 36.3% 98.1% 87.6% 0.0% R V B P Rec. Welfare, ⌥ (^) R 34.1% 30.6% 81.7% 0.0% V B R P Sales (Any Product) 0.776 0.819 0.827 0.750 V R B P Sales (Same Product) 0.403 0.445 0.414 0.375 R V B P Conditional on no provided rating Info. Efficiency -1.0% †^ -5.1% †^ -2.2% †^ 0.0% P B V R Conditional on provided rating View Rate, 1.0 1.0 1.0 0.0 B⇠R⇠V P Info. Efficiency ⌥ 106.6%†^ 100.3% †^ 93.9% 0.0% B R V P Rec. Welfare ⌥ (^) R 100.4%†^ 31.4% 87.6% -6.3% B V R P Sales (Any Product) 0.824 0.821 0.832 0.750 V B R P Conditional on provided rating and sale Sales (Same Product) 0.552 0.543 0.501 0.500 B R V P
Note: †-There are selection effects over quality through the sender’s decision to provide a rating or not, where senders are more likely to send given a high signal. Because of this the efficiency and receiver welfare conditional on no rating can be negative, while they can exceed 100 percent conditional on provision.
the expected receiver outcome w (^) R (Z) relative to no communication, set against an upper bound derived from perfect information exchange. Given selection of the best-case PBE, communication generates 36.3 percent information ef- ficiency in the Baseline, which increases to 98.1 percent in the Receiver treatment.^27 However, the gains in information efficiency do not come for free. While the average sender is much better off in the most-informative Receiver equilibrium than in the Baseline, the provision subsidy has to be paid for. Even though the Receiver treatment increases total efficiency, once we account for the payment they make to the sender, receivers actually fare worse in this parametrization than the Baseline. This is illustrated by the Rec. Welfare row in Table 1, which modifies the efficiency measure to account for the incurred costs of communication to the receiver,
⌥ R =
E (^) ✓ (^) XS ,c S (^) ,!
h u (^) R
⇣ (^) I?(μ? (^) ) (!), ⇢?^ , μ?^ (✓ (^) XS )
⌘i W W W
(c R^ + t ) · Pr {⇢=View, m 2 M} W W
That is, ⌥ (^) R modifies the information efficiency ⌥ to include the receiver’s viewing costs where the t component is the transferred amount, and is directly proportional to a receiver’s expected utility.
(^27) Constraints on the message space, that |M| ⌧ |{A, B} ⇥ ⇥|, does not substantially affect information transfer
here. The four ratings with inferences ⌫ (^) X (m = k (^) X ) > ✓¯ are used to distinguish between choosing the product X and the reservations in! 2 [51, 87].
highest equilibrium sales rate (both overall, and conditional on provision). The reasons behind this are greater provision and the fact that every viewed rating increases receivers’ WTB. In contrast, for the Receiver setting, despite a higher rate of provision, approximately half of the provided rat- ings will convey negative information, which do not affect WTB. Given increased sales relative to both Baseline and Receiver, a large enough profit per sale (or equivalently a large enough quantity of receivers, ⌘) would allow Vendor subsidies to pay for themselves in equilibrium.^32 Finally, the Producer treatment only has a babbling equilibrium outcome. Though ratings are still provided (for non-positive costs c S^ ), receivers choose not to view them, as c R^ > 0 and the rating conveys no useful information—where this same babbling equilibrium is present in all four treatments. Payments conditioned on sales of a particular product are predicted to be counterproductive in the long run, and it is clear that the producers A and B would not want to pay for incentives in equilibrium.^33 To get a sense for how each institution affects the producer X, the Sales (Same Product) rows of Table 1 indicate the fraction of product sales where the receiver chooses the same product as the preceding sender (where Z = X) The same-product recurrence rates are somewhat counter-intuitive: in the Baseline and Re- ceiver treatments, senders are completely aligned with receivers, yet these are the only institutions where viewing a rating leads to significantly greater same-product sales than random choice. There are two reasons for this. The first (and much smaller effect) is that ratings are more likely to be provided when the sender has had a positive experience. The second (and quantitatively larger) component is through the influence of differing ratings on receiver’s WTB, where this effect only exists in the Baseline and Receiver equilibria. When ratings are provided, just under half are neg- ative, but negative ratings still result in an H(✓¯) fraction of the receivers making a purchase (just for the alternative, unrated product). Positive ratings on the other hand, which are sent just over half the time, lead to H (⌫(m)) sales for the rated product, as the positive information increases the receiver’s WTB. Theoretically, all of the increases in total sales from communication in the Baseline and Receiver equilibria accrue to the same product sampled by the sender. In contrast, for Vendor and Producer, the different ratings provided in equilibrium have no effect on receiver’s WTB, and so there is no effect on same-product sales. Within the table, there is an almost neg- ligible same-product sales effect in Vendor, where this stems from slightly higher provision rates when senders observe better-than-average product draws. Our paper’s main hypotheses are the comparative-static orderings between treatments for each outcome variable in Table 1 where the orderings are not affected by moderate levels of risk aver- sion. Table 10 in the appendix provides similar comparisons for risk averse consumers.
4. R ESULTS
Below we present summary results and analysis of data from sessions conducted at the Pitts- burgh Experimental Economics Laboratory. We used z-Tree Fischbacher (2007) experimental soft- ware to collect data from 176 unique subjects across 12 sessions, with 3 sessions per treatment.
(^32) Vendor players have an incentive to secretly provide sale-conditioned incentives in the Receiver and Baseline
environments, as sending glowing reviews is more effective in increasing sales if receivers are completely credulous, and a five rating increases the WTB beyond 60. (^33) However, such incentives deployed secretly in any of the other treatment environments would increase same-
product sales in the short run, holding constant receiver’s behavior. We discuss such shifts in short-run incentives in section 5.
Subjects were paid for two randomly selected rounds out of the 30 they played, with average pay- ments per subject of $18.09. We first outline the treatment averages for the economic variables of interest, and test the comparative statics derived from the most-informative equilibrium pre- dictions. We subsequently go on to detail the behavior of subjects, and outline the “why” of the economic results by examining the component behavior. Finally, in the next section we extend the results with a counterfactual exercise examining long- and short-run effects from changes to our experimental environments.
4.1. Broad Economic Outcomes. Table 2 provides a summary of the main outcome variables in the experiment. Each of the rows provides the sample analog to a prediction in Table 1. How- ever, because the most-informative equilibria have receivers either always or never viewing, we additionally include averages for the subsample with viewed ratings (m (^) it 2 M and ⇢ (^) jt = View). The first five rows in Table 2 outline the unconditional effects for the main economic variables: i) the rate of provision by senders; ii) the overall efficiency of the information transfer, ⌥;^34 iii) the receiver welfare, which accounts for the expected cost of viewing, ⌥ (^) R ; iv) the proportion of receivers opting to make a purchase of any product, Prˆ {Z (^) jt 6 = R}; and v) the proportion of
receivers opting to purchase the same product as the sender, Prˆ {Z (^) jt = X (^) it }. 35 After the unconditional outcomes we provide conditional averages assessed over the rele- vant subsamples. The first conditional measure examines outcomes without a provided rating, where we indicate the information efficiency ⌥ |m (^) ;. The second conditional measure is restricted to rounds with a rating, m (^) it 2 M, where we indicate the proportion of receivers who view, Pr^ ˆ {⇢ (^) jt = View |M}. We next consider only those rounds with exchanged information, and ex- amine the subsample with viewed ratings. Here we parallel the unconditional results, indicating the information efficiency, receiver welfare and both overall and same-product sales levels. How- ever, to make clear the degree to which ratings persuade receivers to purchase the same prod- uct, we also indicate same-product sales conditional on both a viewed rating and any sale, so Pr^ ˆ {Z (^) jt = X (^) it |Z (^) jt 6 = R, M, View}—where random choice would select the same product 1 / 2 the time.
Efficiency of information transfer. Our unconditional efficiency results match the comparative- statics generated by the most-efficient equilibrium predictions. At one end, the Receiver institution produces the most information transfer, with significantly greater efficiency than any other treat- ment. The Producer treatment meanwhile has the lowest information transfer, with an average efficiency just below zero. Between these two extremes are the Vendor and Baseline treatments, in line with their theoretical efficiency rankings. Ordinally, the results indicate that the most- informative equilibrium prediction does quite well. However, once we compare the cardinal levels in Table 1 and 2, we see quantitatively large differences. The Receiver and Vendor treatments theoretically allow for efficiency levels close to the frictionless upper bound, but in realization we end up with just a quarter of the total efficiency possible.
(^34) All efficiency measures are calculated by a recombinant procedure, matching all receivers against the entire sender
population consistent with the information set. In this way, we integrate out much of the exogenous noise (variation in x (^) it |mit and c (^) it ) while retaining the observed strategic variation in sender and receiver behavior. We could further reduce the exogenous noise by focusing on the last 15 rounds and using the supplied cutoffs C (^) it and ⌦ (^) jt to remove variation introduced through G and H but here we provide results over all 30 rounds. (^35) Here, and henceforth, Prˆ {T |S } will denote the sample proportion 1 |S|
P s 2 S 1 {s^2 T }.
One reason for the drop is the large difference in provision and viewing rates from the predicted level in Receiver and Vendor. To control for this we can instead look at the information efficiency conditional on a provided and viewed rating. Examining this subsample in Table 2 we do see a much larger efficiency increase. Receiver and Producer are again the best and worst treatments, respectively. For Receiver we observe an average efficiency of 82 percent of the upper bound, while even the Producer treatment is conveying useful information, with 45 percent efficiency. Conditional on a viewed rating, the Baseline is significantly worse than the Receiver at just 58 percent efficiency, where the best-case theory predicts comparable levels.^36 Instead, we observe a large and significant efficiency gap between Receiver and Baseline, and no significant difference between Vendor and Baseline. Instead of the 94 percent efficiency possible after an equilibrium ratings is provided, we observe just 58 percent in Vendor.
Result 1 (Efficiency). A transfer from Receivers to Senders to defray provision costs leads to significant increases in information transmission. However, this gain is less than theoretically predicted due to lower provision and viewing rates.
Receiver outcomes. For the three treatments where receivers do not pay any additional amount to the sender, the immediate effect of viewing a rating is the same: the receiver pays a 6.3 percent efficiency penalty through the viewing cost c R^. However, in the Receiver treatment, the transfer t to senders reduces receivers’ share of the information surplus substantially— with a 69 percent penalty to efficiency on viewing. Despite this large cost, receiver welfare conditional on viewing is still positive. Net of the costs involved, receivers who view a rating improve their outcomes relative to the expected outcome with no sender, W. Moreover, we will later show that viewers can expect to do better than those choosing not to view, accounting for any selection effects. The most important result with regard to receiver outcomes is that their maximum payoffs are achieved in the Vendor treatment. Conditional on a viewed rating, the receiver welfare row of Table 2 shows that receivers do just as well in the Baseline and Vendor treatments, so the effect of misalignment over WTB in the Vendor incentive seems to be small. Trading off some quality in the information provided in order to subsidize ratings leads to large quantity increases. The unconditional receiver welfare figures therefore attain a maximum in Vendor. However, the overall difference in receiver welfare compared to the Baseline is only marginally significant. The reason for this (and for the comparable efficiencies conditional on a viewed rating) are due to negative efficiency for those receivers who are not provided with a rating. That is, those receivers without a rating do worse than the lower bound level predicted with zero information transfer. This effect is strongest in the Vendor treatment, where the absence of a rating leads to an efficiency level of -39 percent, though the magnitude of this effect in Producer is comparable. As we will later demonstrate when we examine behavior in more detail, the cause of theses drops is that ratings in the incentivized environments are less likely to be provided by senders with bad signals, which depresses final outcomes for receivers without a provided rating (while increasing the outcome for those with a rating).
Result 2 (Receiver Welfare). Decreasing the alignment-of-interest between the sender and re- ceiver can improve receiver welfare, provided the misalignment leads to a compensating increase in rating provision.
(^36) The Baseline is actually predicted to do better than Receiver, conditional on provision, as ratings are relatively
more likely to be provided following a positive draw x than a negative one, where these differences in prediction depend on the shape of cost CDF, G.
Product Sales and Recurrence. Consumers are obviously not the only parties of interest in our setting, as vendors and producers will be affected by changes in purchasing behavior. However, without further assumptions, we are only able to partially address the desirability of each mech- anism to these other participants. The costs incurred in incentivizing ratings relative to any addi- tional revenues through increased sales are not identified, and so we will consider the benefit to marketplaces (and producers) through the total (same product) sales rate. Conditional on a provided rating, we find that the Receiver institution produces the most sales (significantly more than Baseline and Producer, though only marginally significant against Ven- dor), where theory indicates Vendor should drive more sales given a rating. Unconditionally, the greatest sales rate is in the Vendor treatment—as predicted by the theory, though the primary driver here is the greater fraction of viewed ratings—however this difference is not significant. While we do observe that the institutions with the largest sales volumes are indeed Vendor and Receiver, the size of the increase over Baseline and Producer is smaller than predicted. One potential reason for the small sales effect is the specific reservation distribution H chosen for the experiment. Receivers are predicted to choose the outside option only a quarter of the time in uninformative settings, with this number decreasing as the setting becomes more informative. As a result, the possibility for large sales differences is somewhat limited. In section B we examine counterfactual behavior across a family of reservation distributions using the elicited WTB cutoffs in the experiment, where we show that the Vendor environment is more effective at generating new sales as the average reservation increases.
Result 3 (Total Sales). Conditional on a viewed rating, the Receiver environment generates the most sales. However, greater provision and viewing in Vendor lead to similar unconditional sales rates.
Result 3 gives us a coarse description of the desirability of each institutions from the point of view of the vendor player—frequently the party with explicit control over the rating system’s design. The results indicate that the Receiver and Vendor are most effective at inducing new consumers to purchase a new product rather than the outside option. Where Result 3 was about the purchase of any product, other parties might be concerned with the extent to which ratings induce receivers to purchase the same product as the sender. Here our experimental data indicates the polar opposite of the equilibrium predictions. Conditional on a viewed rating, the Producer treatment has the greatest degree of product recurrence, where we should expect to see no difference from random uniform choice across the two competing prod- ucts. In contrast, the Baseline and Receiver treatments experience the lowest same-product sales rates, where theory indicates they should have the most.^37 The success at generating increased product sales suggests that Producer-like incentives can be profitable to specific manufacturers. Conditional on a viewed rating, the Producer environment is far and away the best at generating repeat purchases. However, unconditionally the Vendor and Producer treatments are more compa- rable, with each generating significantly more same-product purchases than the other institutions. Later we will show that though Producer incentives are very effective at capturing market share for the specific product, they are ineffective at growing the overall market size through increased consumer WTB. In comparison, the Vendor incentive does moderately well at both of these goals, generating comparable product recurrence overall.
(^37) The same results hold if we look at recurrence unconditionally, where we observe the order P ?? V B ? R,
ranging from 42.7 percent sales in Producer to 38.4 percent sales in Receiver.
