Projection Equilibrium: Definition and Applications to Social Investment and Persuasion

People exaggerate the extent to which their private information is shared with others. This paper introduces this phenomenon portably into Bayesian games where people wrongly think that if they can condition their strategy on an event others can do as well. I apply the model to a variety of settings. In the context of social investment people misattribute the uncertainty they face about others preferences to others having antagonistic motives. Even if all parties prefer mutual investment, none invests, yet all come to believe that others prefer not to invest. In the context of communication with costly state veri…cation, the model predicts credulity: persuasion by advisors, who are known to have an incentive to exaggerate the quality of an asset, will nevertheless induce uniformly exaggerated average posteriors for receivers. When endogenizing the con‡ict of interest between senders and receivers, I show that such credulous belief-bubbles rise discontinuously as the size of the market or the complexity of the asset increases. Further implications to auctions, common value trade and zero-sum games are explored.