Uncertainty aversion and equilibrium existence in games with incomplete information

Azrieli, Yaron and Teper, Roee (2009): Uncertainty aversion and equilibrium existence in games with incomplete information.

Abstract

We consider games with incomplete information a la Harsanyi, where the payoff of a player depends on an unknown state of nature as well as on the profile of chosen actions. As opposed to the standard model, players' preferences over state--contingent utility vectors are represented by arbitrary functionals. The definitions of Nash and Bayes equilibria naturally extend to this generalized setting. We characterize equilibrium existence in terms of the preferences of the participating players. It turns out that, given continuity and monotonicity of the preferences, equilibrium exists in every game if and only if all players are averse to uncertainty (i.e., all the functionals are quasi--concave). We further show that if the functionals are either homogeneous or translation invariant then equilibrium existence is equivalent to concavity of the functionals.

• Item Type: MPRA Paper
• Language: English
• Keywords: Games with incomplete information, equilibrium existence, uncertainty aversion, convex preferences.
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

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