Games of Incomplete Information Without Common Knowledge Priors
AbstractWe relax the assumption that priors are common knowledge, in the standard model of games of incomplete information. We make the realistic assumption that the players are boundedly rational: they base their actions on finite-order belief hierarchies. When the different layers of beliefs are independent of each other, we can retain HarsÃ¡nyi's type-space, and we can define straightforward generalizations of Bayesian Nash Equilibrium (BNE) and Rationalizability in our context. Since neither of these concepts is quite satisfactory, we propose a hybrid concept, Mirage Equilibrium, providing us with a practical tool to work with inconsistent belief hierarchies. When the different layers of beliefs are correlated, we must enlarge the type-space to include the parametric beliefs. This presents us with the difficulty of the inherent openness of finite belief subspaces. Appealing to bounded rationality once more, we posit that the players believe that their opponent holds a belief hierarchy one layer shorter than they do and we provide alternative generalizations of BNE and Rationalizability. Finally, we show that, when beliefs are degenerate point beliefs, the definition of Mirage Equilibrium coincides with that of the generalized BNE. Copyright Kluwer Academic Publishers 2001
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Bibliographic InfoArticle provided by Springer in its journal Theory and Decision.
Volume (Year): 50 (2001)
Issue (Month): 4 (June)
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Web page: http://www.springerlink.com/link.asp?id=100341
Finite belief hierarchy; Games of incomplete information; Inconsistent beliefs;
Other versions of this item:
- Jozsef Sakovics, 2004. "Games of incomplete information without common knowledge priors," ESE Discussion Papers 77, Edinburgh School of Economics, University of Edinburgh.
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