A Theory of Reciprocity with Incomplete Information

A model of belief dependent preferences in finite multi-stage games with ob- servable actions is proposed. It combines two dissimilar approaches: incomplete information (Levine, 1998) and intentionality (Dufwenberg and Kirchsteiger, 2004; Falk and Fischbacher, 2006). Incomplete information is important because social preferences are not directly observable; intentions are found to be indispensable in explaining behavior in games (Falk, Fehr, and Fischbacher, 2008). In the model it is assumed that the players have social attitudes that define their social pref- erences. In addition, players care differently about the payoffs of other players depending on their beliefs about their social attitude and possibly on the beliefs of higher orders. As the game unfolds players update their beliefs about the types of other players. An action of a player shows intention when she chooses it antic- ipating future belief updating by others. A reasoning procedure is proposed that allows players to understand how to update beliefs by constructing a sequence of logical implications.