Abstract
We provide random equilibrium existence theorems for non-cooperative random games with a countable number of players. Our results yield as corollaries generalized random versions of the ordinary equilibrium existence result of J. Nash [22]. Moreover, they can be used to obtain equilibrium existence results for games with incomplete information, and in particular Bayesian games. In view of recent work on applications of Bayesian games and Bayesian equilibria, the latter results seem to be quite useful since they delineate conditions under which such equilibria exist.
We would like to thank Roko Aliprantis, Erik Balder, Kim Border, Taesung Kim, M. Ali Khan and David Schmeidler for comments, discussions and suggestions. Of course we are responsible for any remaining shortcomings.
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Yannelis, N.C., Rustichini, A. (1991). Equilibrium Points of Non-Cooperative Random and Bayesian Games. In: Positive Operators, Riesz Spaces, and Economics. Studies in Economic Theory, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58199-1_2
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DOI: https://doi.org/10.1007/978-3-642-58199-1_2
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