The standard framework for analyzing games with incomplete information models players as if they have an infinite depth of reasoning. This paper generalizes the type spaces of Harsanyi (1967-1968) so that players can have a finite depth of reasoning. The innovation is that players can have a coarse perception of the higher-order beliefs of other players, thus formalizing the small-world idea of Savage (1954) in a type-space context. Unlike in other models of finite-order reasoning, players with a finite depth of reasoning can reason about higher-order events if these events are generated by events of sufficiently low order. In particular, an event F can be common belief if it is entailed by some public event. This is true even if players cannot reason about higher-order statements like "Ann believes that Bob believes that Ann believes...(58 times)...that F"' in isolation. Thus, the usual equivalence between the iterative and the fixed-point account of common belief breaks down when players have a finite depth, and common belief is easier to attain than as suggested by the iterative approach.
|Original language||English (US)|
|Publisher||Social Science Research Network (SSRN)|
|Number of pages||49|
|State||Published - Jun 24 2012|