Self-recognition in teams

This paper studies an idea we call "(null) self-recognition," which occurs when a player who was certain that they were a particular type privately discovers that they are in fact some other type. To address unresolved questions as to how players update their beliefs regarding their partner's type and higher-order beliefs regarding both players' types after self-recognition, we propose a "sequential reassessment" rule, in which beliefs concerning each player's type are modified up to a given order. As an initial investigation of its equilibrium consequences, we embed sequential reassessment in a simple model of team production, in which players experience self-recognition when game play begins. Our main result, which applies for team projects with uneven task demands, shows how a player's decision to work or shirk can depend solely on whether that player's reassessment of their own type is "deeper" or "shallower" than their reassessment of their partner's type.