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Rational exaggeration and counter-exaggeration in information aggregation games

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  • Gordon Rausser
  • Leo Simon

    ()

  • Jinhua Zhao

Abstract

We study an information aggregation game in which each of a finite collection of “senders” receives a private signal and submits a report to the center, who then makes a decision based on the average of these reports. The integration of three features distinguishes our framework from the related literature: players’ reports are aggregated by a mechanistic averaging rule, their strategy sets are intervals rather than binary choices, and they are ex ante heterogeneous. In this setting, players engage in a “tug-of-war,” as they exaggerate and counter-exaggerate in order to manipulate the center’s decision. While incentives to exaggerate have been studied extensively, the phenomenon of counter-exaggeration is less well understood. Our main results are as follows. First, the cycle of counter-exaggeration can be broken only by the imposition of exogenous bounds on the space of admissible sender reports. Second, in the unique pure-strategy equilibrium, all but at most one player is constrained with positive probability by one of the report bounds. Our third and fourth results hold for a class of “anchored” games. We show that if the report space is strictly contained in the signal space, then welfare is increasing in the size of the report space, but if the containment relation is reversed, welfare is independent of the size of the space. Finally, the equilibrium performance of our heterogeneous players can be unambiguously ranked: a player’s equilibrium payoff is inversely related to the probability that her exaggeration will be thwarted by the report bounds. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Gordon Rausser & Leo Simon & Jinhua Zhao, 2015. "Rational exaggeration and counter-exaggeration in information aggregation games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 109-146, May.
  • Handle: RePEc:spr:joecth:v:59:y:2015:i:1:p:109-146
    DOI: 10.1007/s00199-015-0870-2
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    References listed on IDEAS

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    Cited by:

    1. Rosar, Frank, 2015. "Continuous decisions by a committee: Median versus average mechanisms," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 15-65.
    2. David Court & Benjamin Gillen & Jordi McKenzie & Charles R. Plott, 2018. "Two information aggregation mechanisms for predicting the opening weekend box office revenues of films: Boxoffice Prophecy and Guess of Guesses," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 25-54, January.

    More about this item

    Keywords

    Information aggregation; Majority rule; LIBOR; Baltic Dry Index; Yelp; Online reviews; Exaggeration; Counter-exaggeration; Mean versus median mechanism; Strategic communication; Incomplete-information games; Strategic information transmission; F71; D72; D82;

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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