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On a Theorem by Mas-Colell

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Carmona, Guilherme

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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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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. M Ali Khan & Kali P Rath & Yeneng Sun, 1994. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economics Working Paper Archive 381, The Johns Hopkins University,Department of Economics, revised Feb 1997.
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  2. Carmona, Guilherme, 2004. "On the Existence of Pure Strategy Nash Equilibria in Large Games," FEUNL Working Paper Series wp465, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
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  3. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653. [Downloadable!] (restricted)
  4. Hart, Sergiu & Hildenbrand, Werner & Kohlberg, Elon, 1974. "On equilibrium allocations as distributions on the commodity space," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 159-166, August. [Downloadable!] (restricted)
  5. M Ali Khan & Yeneng Sun, 2002. "Non-Cooperative Games with Many Players," Economics Working Paper Archive 482, The Johns Hopkins University,Department of Economics. [Downloadable!]
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