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 beyond the central result of E. J. Balder (1995, Int. J. Game Theory 24, 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. Theory 77, 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. © 2002 Elsevier Science