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Bounded Reasoning and Higher-Order Uncertainty

  • Willemien Kets

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.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1547.

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Date of creation: 19 Mar 2012
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Handle: RePEc:nwu:cmsems:1547
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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. Alfredo Di Tillio, 2006. "Subjective Expected Utility in Games," Working Papers 311, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
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