Competition in Persuasion - PowerPoint Presentation

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Competition in Persuasion

Gentzkow and Kamenica (Restud 2017)

L22Slide2

Research questions

Competition among senders fosters information transmission

(Krishna and Morgan 2001, Battaglini 2002, Ambrus and Lu 2009)Robust fully revealing BNE with 2 sendersBubbling equilibriumDoes competition among senders also improve transmission when senders maximize ex ante welfarecommit to revealing signalsIn particular:Informativeness of equilibrium relative to a collusive benchmarkSimple characterization of equilibrium set Slide3

Motivating example

Senders: 2 pharmaceutical firms, maximize market share for their drugs

Receivers: consumers (unit mass)for each consumer efficacy of drug is mass 0.5 buys drug with higher expected efficacymass 0.5 buys better drug only if that reveals efficacy of a drug Two variants of a gameA firm can commit to revealing test results for own drug (Game 1)A firm can commit to revealing results for arbitrary tests (Game 2)Slide4

Game 1 (own drug tests)

Firm can chose two ``strategies’’

Demands (payoffs)Nash: Collusive outcomeObservations:Competition: less than full revelation informationCompetitive outcome less informative than collusive outcomeSlide5

Game 2 (testing both drugs)

Each firm has four strategies

Demands (payoffs)Nash vs collusive outcomeNash outcome as informative as collusive oneSlide6

Lessons

What structure drives the predictions in both games?

In Game 2 none of the firms has a monopoly on a particular piece of informationThis feature of information structure is called Blackwell connectedness The game becomes of a provision of free public goodIn what follows:We define a game that captures competition in persuasionIntroduce a notion of Blackwell connectednessDemonstrate information aggregation resultGive some other results Slide7

Simultaneous move (persuasion) game

State space , common prior

Signal Game:Players: senders Strategies: , available signalsFor its outcome is a distribution over posteriorsPayoffs:ExampleSlide8

Important outcomes

Feasible outcome

Set of feasible outcomesEquilibrium outcome Collusive outcomeWe assume that is unique Slide9

Blackwell connectedness

Blackwell partial order on set feasible outcomes

Two signals are equivalent if D: Set is Blackwell connected if for anyInterpretation: Each sender can provide as much information as other players combinedNo player has exclusivity in providing particular type of informationEach player has to be able to exactly match the benchmark Slide10

Blackwell Connected S: examples

Independent draws: each player choses a number of i.i.d. draws from some fixed distribution. Aggregate information

Facts: Each player choses which facts to uncover. , aggregate informationPrecision: each player choses All or nothing: In these examples Blackwell order is complete on Slide11

Lower bound on equilibrium

informativenessP: (for all preferences) iff

is Blackwell connected Remark:For BC strategy space either or. not comparableIn the examples Blackwell order is completeIn the latter competition is good for information transmissionIndependent tests of drugs: collusion hurts information transmissionOther examplesSlide12

Proof

If

Only ifSlide13

Equilibrium set

For the remaining results assume:

Identical strategy setsBlackwell connectedness Slide14

Characterization of equilibrium set

D: For sender outcome is unimprovable if for any feasible

one has P: A feasible outcome I. is an equilibrium outcome iff it is unimprovable for allRemark: Equilibrium set can be determined as an intersection of unimprovable sets for all playersSlide15
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Other results

Suppose there exists feasible. such that

P: is an equilibrium outcomeProof: is trivially unimprovableConsider least informative equilibrium (minimal equilibrium)Informativess of minimal equilibrium is non-decreasing in number of playersmisalignment of players preferences