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On a Theorem by Mas-Colell

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  • Carmona, Guilherme

Abstract

We consider anonymous games with a Lebesgue space of players in which either the action space or players' characteristics are denumer- able. Our main result shows that the set of equilibrium distributions over actions coincides with the set of distributions induced by equilib- rium strategies. This result, together with Mas-Colell (1984)'s theorem, implies that any continuous, denumerable game has an equilibrium strategy. In particular, the theorems of Khan and Sun (1995) and Khan, Rath, and Sun (1997) can be obtained as corollaries of Mas-Colell's.

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Bibliographic Info

Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp485.

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Length: 35 pages
Date of creation: 2006
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Handle: RePEc:unl:unlfep:wp485

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  1. HART, Sergiu & HILDENBRAND, Werner & KOHLBERG, Elon, . "On equilibrium allocations as distributions on the commodity space," CORE Discussion Papers RP -183, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Guilherme Carmona, 2004. "On the Existence of Pure Strategy Nash Equilibria in Large Games," Game Theory and Information 0412008, EconWPA.
  3. M Ali Khan & Yeneng Sun, 1996. "Non-Cooperative Games with Many Players," Economics Working Paper Archive 382, The Johns Hopkins University,Department of Economics.
  4. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
  5. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
  6. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer, vol. 2(3), pages 427-33, July.
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