Abstract:

Inherent in standard game-theoretic models is that players have infinite hierarchies of beliefs, that is, beliefs about the state of nature, beliefs about others' beliefs about nature, and so on. Can the standard framework nevertheless be used to model situations in which players potentially have a finite depth of reasoning? This paper extends the standard Harsanyi framework to allow for higher-order uncertainty about players' depth of reasoning. The basic principle is that players with a finite depth of reasoning cannot distinguish states that differ only in players' beliefs at high orders. I apply the new framework to the electronic mail game of Rubinstein (1989). Coordination on the Pareto-efficient action is possible when there is higher-order uncertainty about players' depth of reasoning, unlike in the standard case, provided that one player thinks it is sufficiently likely that the other player has a finite (though potentially very high) depth of reasoning. Finally, I construct a type space that allows for bounded reasoning that contains the universal type space (which generates all infinite belief hierarchies) as a subspace, showing that the present framework fully generalizes the Harsanyi formalism.