A Unifying Pair of Cournot–Nash Equilibrium Existence Results

For games with a measure space of players a tandem pair, consisting of a mixed and a pure Cournot–Nash equilibrium existence result, is presented. Their generality causes them to be completely mutually equivalent. This provides a unifying pair of Cournot–Nash existence results that goes considerably...

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Bibliographic Details
Published in:Journal of economic theory 2002-02, Vol.102 (2), p.437-470
Main Author: Balder, Erik J.
Format: Article
Language:English
Subjects:
Bayesian Nash equilibrium
differential information
Econometrics
Economic theory
Equilibrium
equilibrium distribution
Game theory
mixed Cournot–Nash equilibrium
pure Cournot–Nash equilibrium
Studies
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Summary:For games with a measure space of players a tandem pair, consisting of a mixed and a pure Cournot–Nash equilibrium existence result, is presented. Their generality causes them to be completely mutually equivalent. This provides a unifying pair of Cournot–Nash existence results that goes considerably beyond the central result of E. J. Balder (1995, Int. J. Game Theory24, 79–94, Theorem 2.1). The versatility of this pair is demonstrated by the following new applications: (i) unification and generalization of the two equilibrium distribution existence results by K. P. Rath (1996, J. Math. Econ.26, 305–324) for anonymous games, (ii) generalization of the equilibrium existence result of T. Kim and N. C. Yannelis (1997, J. Econ. Theory77, 330–353) for Bayesian differential information games, (iii) inclusion of the Bayesian Nash equilibrium existence results of P. R. Milgrom and R. J. Weber (1985, Math. Oper. Res.10, 619–632) and E. J. Balder (1988, Math. Operations Res.13, 265–276) for games with private information in the sense of J. C. Harsanyi (1967, Manage. Sci.14, 159–182). Journal of Economic Literature Classification Number: C72.
ISSN:0022-0531
1095-7235
DOI:10.1006/jeth.2001.2849