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Games of incomplete information without common knowledge priors

  • Jozsef Sakovics

    ()

We 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 Harsányi’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.

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File URL: http://www.econ.ed.ac.uk/papers/games_of_incomplete_info_JS.pdf
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Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 77.

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Length: 15
Date of creation: Mar 2004
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Handle: RePEc:edn:esedps:77
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  1. Hyun Song Shin & Andrew Postlewaite & Stephen Morris, 1995. "Depth of knowledge and the effect of higher order uncertainty," Economic Theory, Springer, vol. 6(3), pages 453-467.
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  13. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
  14. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  15. Offerman, Theo & Sonnemans, Joep & Schram, Arthur, 1996. "Value Orientations, Expectations and Voluntary Contributions in Public Goods," Economic Journal, Royal Economic Society, vol. 106(437), pages 817-45, July.
  16. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
  17. Camerer, Colin & Weigelt, Keith, 1991. "Information Mirages in Experimental Asset Markets," The Journal of Business, University of Chicago Press, vol. 64(4), pages 463-93, October.
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