Incomplete Information Aggregation Games

This paper concerns a class of collective decision-making problems under incomplete information. Members of a group receive private signals and the group must take a collective decision—e.g., make a group purchase—based on the aggregate of members’ private information. Since members have diverse preferences over the outcome of this decision, each has an incentive to manipulate the decision-making process by mis-reporting his private information. Whenever there are natural bounds on the set of admissible reports—e.g., if one’s signal is one’s endowment, one cannot report a negative signal—an asymmetry arises between those who would over-report, and those who would under-report, their true information. To model the incentives to misreport, and the associated asymmetry, we introduce a new kind of incomplete information game called an aggregation game. In such a game, each player is characterized by two parameters: the first—the player’s type—is privately known, the second is publicly observed. Players simultaneously report their types, resulting in an outcome, which is a function of the aggregate of these reports. Each player’s payoff depends on his observable characteristic, the aggregate of players’ type realizations and the game’s outcome. Every aggregation game has a pure-strategy equilibrium. We characterize these equilibria, and study their comparative statics properties, under a variety of restrictions. JEL classification: F71, D72, D82.