Projection Equilibrium: Definition and Applications to Social Investment and Persuasion

People exaggerate the extent to which their information is shared with others. I introduce such information projections into a large class of Bayesian games where people wrongly think that if they can condition their strategy on an event others can as well. I apply the model to a variety of settings. In the context of social investment, people misattribute the uncertainty others face about their preferences into others having antagonistic preferences. Even if all parties prefer mutual investment, none invests, but comes to believe through interacting with others that she is alone preferring mutual investment. In the context of communication, the model predicts credulity: persuasion by an advisor with a known incentive to lie will nevertheless induce uniformly inflated average posteriors. Complexity of an asset, but greater financial education as well, can enhance such credulity. I extend the model to incorporate ignorance projection and re- late the predictions of projection equilibrium to evidence on common-value trade. Here, consistent with the evidence in Samuelson and Bazerman (1985), the model predicts non-altruistic truth-telling by sellers. For buyers it predicts the winner?s curse and provides a better fit of the data than BNE or cursed equilibrium. Further applications to zero-sum games and auctions are explored.