Rational exaggeration in information aggregation games
This paper studies a class of information aggregation models which we call â€œaggregation games.â€ 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 aggregation game is that heterogeneous players engage in a â€œtug-of-war,â€ as they attempt to manipulate the centerâ€™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 exaggerate to the maximum admissible extent, regardless of their individual signals. In the limit, the connection between playersâ€™ private information and the outcome of the game is obliterated.
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