| Abstract: |
The standard framework for analyzing games with incomplete information models
players as if they form beliefs about their opponents' beliefs about their
opponents' beliefs and so on, that is, as if players have an infinite depth of
reasoning. This strong assumption has nontrivial implications, as is
well-known. This paper therefore generalizes the type spaces of Harsanyi
(1967-1968) to model 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 the case in other models of
finite-order reasoning, players with a finite depth of reasoning can have
nontrivial higher-order beliefs about certain events. Intuitively, some
higher-order events are generated by events of lower orders, making it
possible for players to reason about them, even if they have a finite depth of
reasoning. |