On Cournot-Nash equilibria in generalized qualitative games with an atomless measure space of agents

Khan, M. Ali; Papageorgiou, Nikolaos S.

doi:10.1090/S0002-9939-1987-0891154-5

On Cournot-Nash equilibria in generalized qualitative games with an atomless measure space of agents
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by M. Ali Khan and Nikolaos S. Papageorgiou PDF

Proc. Amer. Math. Soc. 100 (1987), 505-510 Request permission

Abstract:

We present a result on the existence of Cournot-Nash equilibria in games with an atomless measure space of players each with nonordered preferences and with strategy sets in a separable Banach space. Our result dispenses with any convexity assumption on the preference correspondence.

References

Topological spaces

C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, Vol. 580, Springer-Verlag, Berlin-New York, 1977. MR 0467310

Linear operators

A comment on Khan-Vohra

A. N. Kolmogorov and S. V. Fomin, Introductory real analysis, Revised English edition, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1970. Translated from the Russian and edited by Richard A. Silverman. MR 0267052
M. Ali Khan, On extensions of the Cournot-Nash theorem, Advances in equilibrium theory (Indianapolis, Ind., 1984) Lecture Notes in Econom. and Math. Systems, vol. 244, Springer, Berlin, 1985, pp. 79–106. MR 873761, DOI 10.1007/978-3-642-51602-3_{5}
M. Ali Khan, Equilibrium points of nonatomic games over a Banach space, Trans. Amer. Math. Soc. 293 (1986), no. 2, 737–749. MR 816322, DOI 10.1090/S0002-9947-1986-0816322-3
M. Ali Khan and Nikolaos S. Papageorgiou, On Cournot-Nash equilibria in generalized qualitative games with a continuum of players, Nonlinear Anal. 11 (1987), no. 6, 741–755. MR 893778, DOI 10.1016/0362-546X(87)90040-X
M. Ali Khan and Rajiv Vohra, Equilibrium abstract economies without ordered preferences and with a measure space of agents, J. Math. Econom. 13 (1984), no. 2, 133–142. MR 758569, DOI 10.1016/0304-4068(84)90013-2

Equilibria in abstract economies with a measure space and with an infinite dimensional strategy space

On a Carathéodory-type selection theorem

Nikolaos S. Papageorgiou, Representation of set valued operators, Trans. Amer. Math. Soc. 292 (1985), no. 2, 557–572. MR 808737, DOI 10.1090/S0002-9947-1985-0808737-3
David Schmeidler, Equilibrium points of nonatomic games, J. Statist. Phys. 7 (1973), 295–300. MR 465225, DOI 10.1007/BF01014905
Wayne Shafer and Hugo Sonnenschein, Equilibrium in abstract economies without ordered preferences, J. Math. Econom. 2 (1975), no. 3, 345–348. MR 398464, DOI 10.1016/0304-4068(75)90002-6
Nicholas C. Yannelis, Equilibria in noncooperative models of competition, J. Econom. Theory 41 (1987), no. 1, 96–111. MR 875986, DOI 10.1016/0022-0531(87)90007-X
Nicholas C. Yannelis and N. D. Prabhakar, Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econom. 12 (1983), no. 3, 233–245. MR 743037, DOI 10.1016/0304-4068(83)90041-1