On a Theorem by Mas-Colell
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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| Length: | 35 pages |
| Date of creation: | 2006 |
| Handle: | RePEc:unl:unlfep:wp485 |
| Contact details of provider: | Postal: Campus de Campolide, 1099-032 Lisboa Phone: (351) 21 3801638 Fax: (351) 21 3870933 Web page: http://www.fe.unl.pt Email: More information through EDIRC
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- 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.
- 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.
- 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.
- HART, Sergiu & HILDENBRAND, Werner & KOHLBERG, Elon, "undated". "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).
- Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
- Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808 Elsevier.
- M Ali Khan & Yeneng Sun, 1996. "Non-Cooperative Games with Many Players," Economics Working Paper Archive 382, The Johns Hopkins University,Department of Economics.
- Khan, A. & Sun, Y., 2000. "Non-Cooperative Games with Many Players," Papiers d'Economie Mathématique et Applications 2000.80, Université Panthéon-Sorbonne (Paris 1).
- M Ali Khan & Yeneng Sun, 2002. "Non-Cooperative Games with Many Players," Economics Working Paper Archive 482, The Johns Hopkins University,Department of Economics.
- Guilherme Carmona, 2004. "On the Existence of Pure Strategy Nash Equilibria in Large Games," Game Theory and Information 0412008, EconWPA.
- 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.
- Carmona, Guilherme, 2006. "On the Existence of Pure Strategy Nash Equilibria in Large Games," FEUNL Working Paper Series wp487, Universidade Nova de Lisboa, Faculdade de Economia.
- Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(3), pages 427-433, July. Full references (including those not matched with items on IDEAS)
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