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Unformatted text preview: Electronic copy available at: http://ssrn.com/abstract=1279601 RATIONAL EXAGGERATION IN INFORMATION AGGREGATION GAMES GORDON C. RAUSSER, LEO K. SIMON, AND JINHUA ZHAO ABSTRACT. This paper studies a class of information aggregation models which we call “aggrega- tion games.” It departs from the related literature in two main respects: information is aggregated by averaging rather than majority rule, and each player selects from a continuum of reports rather than making a binary choice. Each member of a group receives a private signal, then submits a report to the center, who makes a decision based on the average of these reports. The essence of an aggre- gation game is that heterogeneous players engage in a “tug-of-war,” as they attempt to manipulate the center’s decision process by mis-reporting their private information. When players have distinct biases, almost of them rationally exaggerate the extent of these biases. The degree of exaggeration increases with the number of players: if the game is sufficiently large, then almost all players ex- aggerate to the maximum admissible extent, regardless of their individual signals. In the limit, the connection between players’ private information and the outcome of the game is obliterated. Keywords: information aggregation; majority rule; proportional representation; mean versus me- dian mechanism; strategic communication; incomplete information games; strategic information transmission JEL classification: F71, D72, D82. Date : October 2, 2008 . The authors are, respectively, Robert Gordon Sproul Distinguished Professor, Adjunct Professor and Associate Professor. Rausser and Simon are at the Department of Agricultural and Resource Economics, University of California at Berkeley. Zhao is at the Department of Economics and the Department of Agricultural, Food and Resource Economics, Michigan State University. Acknowledgements: Electronic copy available at: http://ssrn.com/abstract=1279601 1. INTRODUCTION We consider a class of games that are naturally characterized as aggregation games . There is a finite collection of players. Each player is characterized by two parameters: the first is a privately observed signal, identified with the player’s type ; the second is an observable characteristic, such as a voting record, profession, income or location. Players’ types are continuously distributed on a compact interval and the distribution of types is common knowledge. Players simultaneously observe their signals, then make reports to a central authority, who makes a decision which affects all of them. Reports are restricted to lie in a compact interval. The authority’s decision rule is fixed and commonly known. The defining property of an aggregation game is that two of its key components—the central authority’s decision and players’ utilities—depend on players’ realized types only through the mean of these realizations. Specifically, a player’s strategy in an aggregation game is to make a report based on his type. The center maps the mean of these reports, paired withgame is to make a report based on his type....
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