Rational Exaggeration in Information Aggregation Games

This paper studies a class of decision-making problems under incomplete information which we call “aggregation games.” It departs from the mainstream information aggregation literature in two 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. Both signals and reports are drawn from compact intervals. Each player’s payoff depends on the center’s decision, the average of players’ signals, and an observable characteristic, interpreted as the player’s bias. The essence of an aggregation game is that heterogeneous players are engaged in “tug-of-war,” as they attempt to influence the center’s decision by mis-reporting their private information. Every aggregation game has a pure-strategy equilibrium, in which players’ strategies are monotonic in their observable characteristics. When players have distinct biases, almost everyone mis-reports his private information in order to manipulate the decision-making process; moreover, almost everyone rationally exaggerates the extent of his bias. The degree of exaggeration increases with the number of players: if the game is sufficiently large, then almost everyone exaggerates to the maximum possible extent, regardless of his individual signal. This result highlights a striking difference between the majority rule and averaging mechanisms: under a wide variety of conditions, the former is an asymptotically perfect aggregator of individuals’ private information; under the latter, by contrast, the connection between players’ private information and the outcome of the game is asymptotically obliterated.