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Competition in Persuasion - Booth School of Business

[17:21 2/12/2016 ]RESTUD: The Review of Economic StudiesPage: 300 300 322 Review of Economic Studies (2017)84, 300 322 The Author 2016. Published by Oxford University Press on behalf of The Review of Economic Studies access publication 18 October 2016 Competition in PersuasionMATTHEW GENTZKOWS tanford University and NBERandEMIR KAMENICAU niversity of ChicagoFirst version received September2012; final version accepted September2016 (Eds.)We study symmetric information games where a number of senders choose what information tocommunicate. We show that the impact of Competition on information revelation is ambiguous in identify a condition on the information environment ( set of signals available to each sender) thatis necessary and sufficient for equilibrium outcomes to be no less informative than the collusive outcome,regardless of preferences.

GENTZKOW & KAMENICA COMPETITION IN PERSUASION 301 for that firm’s drug. The firms maximize the number of consumers buying their drugs. We can represent this situation as the following normal form game:2 null reveal2 null.25,.25.40,.20 reveal1.20,.40.34,.34 This is a Prisoner’s Dilemma. Revealing information is beneficial for the firms ...

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Transcription of Competition in Persuasion - Booth School of Business

1 [17:21 2/12/2016 ]RESTUD: The Review of Economic StudiesPage: 300 300 322 Review of Economic Studies (2017)84, 300 322 The Author 2016. Published by Oxford University Press on behalf of The Review of Economic Studies access publication 18 October 2016 Competition in PersuasionMATTHEW GENTZKOWS tanford University and NBERandEMIR KAMENICAU niversity of ChicagoFirst version received September2012; final version accepted September2016 (Eds.)We study symmetric information games where a number of senders choose what information tocommunicate. We show that the impact of Competition on information revelation is ambiguous in identify a condition on the information environment ( set of signals available to each sender) thatis necessary and sufficient for equilibrium outcomes to be no less informative than the collusive outcome,regardless of preferences.

2 The same condition also provides an easy way to characterize the equilibrium setand governs whether introducing additional senders or decreasing the alignment of senders preferencesnecessarily increases the amount of information words: Communication, Collusion, Information revelationJEL Codes: D831. INTRODUCTIONDoes Competition increase the amount of information revealed? A long tradition in political andlegal thought holds that the answer is yes. This view has motivated protection of freedom ofspeech and freedom of the press, media ownership regulation, the adversarial judicial system,and many other theory indeed suggests several mechanisms through which Competition can increaseinformation revelation ( and Roberts, 1986; Shin, 1998; Battaglini, 2002), but theseresults do not imply that Competition must increase information in all settings, as the followingexample makes are two pharmaceutical companiesj=1,2 each of which produces a drug, anda unit mass of potential consumers indexed byi.

3 For a given consumeri, drugjmay haveeither low or high efficacy, which we represent by ij {l,h}, withPr( ij=h)= , distributedindependently across consumers and drugs. All consumers prefer high efficacy and are otherwiseindifferent between the drugs, but they differ in their outside options: half always buy whicheverdrug has the higher expected efficacy, while the other half buy the better drug only if itsPr( ij=h)is greater than The share of these two types is independent of firmjsimultaneously chooses one of two disclosure policies: a completely uninformativesignal(null), or a fully informative one(revealj)that allows each consumerito determine ij1. See Gentzkow and Shapiro (2008) and references cited [17:21 2/12/2016 ]RESTUD: The Review of Economic StudiesPage: 301 300 322 GENTZKOW & KAMENICACOMPETITION IN PERSUASION301for that firm s drug.

4 The firms maximize the number of consumers buying their drugs. We canrepresent this situation as the following normal form ,. ,. ,. ,.34 This is a Prisoner s Dilemma. Revealing information is beneficial for the firms joint profitsas it increases expected profits from the consumers who buy only ifPr( ij=h)> (Thoseconsumers never buy unless given information.) But revealing information is unilaterallyunattractive since it disadvantages the revealing firm in the Competition for the consumers whoalways buy. The uninformative signal is thus a dominant strategy and the unique equilibriumyields no information. In contrast, if the firms were to collude and maximize the sum of theirpayoffs, they would choose(reveal1,reveal2).

5 In this example, Competition between the firms decreases information revelation and lowersconsumer welfare. Note that the situation would be different if firms could disclose informationnot only about their own drug, but also about their competitor s drug each firm couldchoose reveal1and/or reveal2. In this case, each firm would prefer to unilaterally disclose theefficacy of their competitor s drug, and full revelation would be an main contribution of this article is to identify a necessary and sufficient condition on theinformation environment ( set of signals available to each sender) under which competitioncannot decrease information revelation. We consider a setting where senders with a common priorsimultaneously conduct costless, publicly observed experiments ( signals ) about an unknownstate of the world.

6 The information revealed by these signals can be succinctly summarized by theinduced distribution of posterior beliefs (Blackwell, 1953). We refer to this distribution of beliefsas theoutcomeof the game. We allow senders to have arbitrary utility functions over say that an information environment isBlackwell-connectedif for any profile of others strategies, each sender can unilaterally deviate to any feasible outcome that is more that the environment in the example above is not Blackwell-connected, because startingfrom(null,null), firm 1 cannot unilaterally deviate to induce the more informative outcomeproduced by(null,reveal2). The modified game where firms can disclose information about theircompetitors is Blackwell-connected.

7 More generally, whenever the information environment isBlackwell-connected, any individual sender can generate as much information as all main result shows that the collusive outcome cannot be strictly more informative thanan equilibrium outcome (regardless of preferences) if and only if the information environment isBlackwell-connected. Moreover, when the environment is Blackwell-connected and all sendershave access to the same set of signals, there is a simple way to characterize the set of pure-strategyequilibrium on the example above, we might ask more generally whether a joint venture betweentwo pharmaceutical companies that allows them to coordinate decisions about clinical trials wouldresult in consumers becoming more or less informed about the quality of the firms drugs.

8 If eachfirm can commission a range of clinical trials about the efficacy of both drugs, the environment isBlackwell-connected, and our result implies that the joint venture could only reduce consumers 2. For example, under(null,reveal2), firm 1 never gets consumers with a high outside option and gets (when 2jis revealed to be low) of the half who always buy, so its expected sales are Meanwhile, firm 2 gets each consumerwith probability (when 2jis revealed to be high), so its sales are [17:21 2/12/2016 ]RESTUD: The Review of Economic StudiesPage: 302 300 322302 REVIEW OF ECONOMIC STUDIES information. In contrast, if each firm can conduct clinical trials only about its own drug, theinformation environment is not Blackwell-connected, so there are some demand systems forwhich the joint venture will make consumers more informed.

9 We develop this example in moredetail also analyse two other notions of increased Competition : adding senders and decreasingthe alignment of senders preferences. When considering these additional comparative statics,we restrict our attention to situations where each sender has access to the same set of signalsand we focus on minimally informative, orminimal,equilibria. (These equilibria have somedesirable properties we discuss below.) We find that if the environment is Blackwell-connected,neither introducing additional senders nor increasing preference misalignment can decrease theinformativeness of minimal simplify our main comparative statics, we assume that the collusive outcome is unique, andwe focus on minimal equilibria when we vary the number of senders or preference alignment.

10 InSection 7, we drop these assumptions and state our comparative statics using set comparisons. Wealso show that the Blackwell-connectedness condition can be weakened if we restrict attention tomonotone preferences. Finally, we briefly discuss mixed strategy equilibria and non-Blackwellinformation work connects to several strands of existing literature. First, our analysis relates to workon multi-sender communication ( and Roberts, 1986; Krishna and Morgan, 2001;Battaglini, 2002).3 Our model differs from this literature in three ways. First, senders informationin our model is endogenous, but we abstract from incentive compatibility issues in disclosure,such as those that arise in cheap talk models ( and Sobel, 1982) and persuasiongames with verifiable information ( , 1981; Milgrom, 1981; Milgrom and Roberts,1986; Bull and Watson, 2004; Kartik and Tercieux, 2012).


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