Projection Equilibrium: Denition and Applications to Social Investment and Persuasion

People exaggerate the extent to which their information is shared with others. I incorporate such information projections into general Bayesian games whereby people wrongly think that if they can condition their strategy on an event, others can as well. In the context of social investment, the model predicts that a player misattributes behavior that is due to di¤erences in information to behavior that is due to antagonistic preferences. Even if all players prefer mutual investment, no one invests but each player comes to believe that she is alone in preferring mutual investment. In the context of communication, the model predicts credulity: persuasion by an advisor with a known incentive to exaggerate the truth induces uniformly in‡ated average posteriors. An increase in the complexity of an asset, but also greater …nancial education, can enhance such credulity and reduce welfare. I extend the model to incorporate ignorance projection as well and relate the predictions of projection equilibrium to evidence on commonvalue trade. Consistent with the evidence, Samuelson and Bazerman (1985), the model predicts that sellers engage in too much truth-telling and buyers are subject to the winner’s curse and the loser’s curse, and it provides a better …t of the data than BNE or cursed equilibrium. Further applications to auctions and zero-sum games are explored.