论文信息 - Finitely additive and epsilon Nash equilibria

Finitely additive and epsilon Nash equilibria

We prove the existence of a mixed strategy Nash equilibrium in normal form games when the space of mixed strategies consists of finitely additive probability measures. It is then proved that from this result an existence result for epsilon equilibria with countably additive mixed strategies can be obtained. These results are applied to the classic Cournot game.

Massimo Marinacci | M. Marinacci

[1] J. Mertens,et al. ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

[2] K. Yosida,et al. Finitely additive measures , 1952 .

[3] I. Glicksberg. A FURTHER GENERALIZATION OF THE KAKUTANI FIXED POINT THEOREM, WITH APPLICATION TO NASH EQUILIBRIUM POINTS , 1952 .

[4] R. Aumann. Correlated Equilibrium as an Expression of Bayesian Rationality Author ( s ) , 1987 .

[5] P. Billingsley,et al. Convergence of Probability Measures , 1969 .

[6] V. Crawford. Equilibrium without independence , 1990 .

[7] K. Fan. Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[8] T. H. Hildebrandt,et al. On bounded linear functional operations , 1934 .

[9] E. Maskin,et al. The Existence of Equilibrium in Discontinuous Economic Games, I: Theory , 1986 .

[10] Teddy Seidenfeld,et al. A Fair Minimax Theorem for Two-Person (Zero-Sum) Games Involving Finitely Additive Strategies , 1996 .

[11] W. A. J. Luxemburg,et al. Integration with Respect to Finitely Additive Measures , 1991 .

[12] B. M. Hill,et al. Theory of Probability , 1990 .

[13] Maxwell B. Stinchcombe,et al. Equilibrium Refinement for Infinite Normal-Form Games , 1995 .

[14] W. Novshek. On the Existence of Cournot Equilibrium , 1985 .