This paper studies a class of information aggregation models which we call “aggregation 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 aggregation 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 exaggerate 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.