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On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players

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  • Khan, M. Ali
  • Rath, Kali P.
  • Sun, Yeneng

Abstract

We present results on the existence of pure strategy Nash equilbria in nonatomic games We also show by means of counterexamples that the stringent conditions on the cardinality of actions sets cannot be relaxed and thus resolve questions which have remained open since Schmeidler's 1973 paper

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File URL: http://www.sciencedirect.com/science/article/B6WJ3-45S9359-M/2/1b38d9f5cebd89e018e6dc2271990228
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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 76 (1997)
Issue (Month): 1 (September)
Pages: 13-46

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Handle: RePEc:eee:jetheo:v:76:y:1997:i:1:p:13-46

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
  2. Jovanovic, Boyan & Rosenthal, Robert W., 1986. "Anonymous Sequential Games," Working Papers 86-12, C.V. Starr Center for Applied Economics, New York University.
  3. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
  4. Rustichini, Aldo & Yannelis, Nicholas C., 1991. "Edgeworth's conjecture in economies with a continuum of agents and commodities," Journal of Mathematical Economics, Elsevier, vol. 20(3), pages 307-326.
  5. Bergin, James & Bernhardt, Dan, 1992. "Anonymous sequential games with aggregate uncertainty," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 543-562.
  6. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346.
  7. Rob, Rafael, 1987. "Entry, Fixed Costs and the Aggregation of Private Information," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 619-30, October.
  8. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
  9. 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.
  10. Bewley, Truman F, 1973. "The Equality of the Core and the Set of Equilibria in Economies with Infinitely Many Commodities and a Continuum of Agents," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 383-94, June.
  11. Peleg, Bezalel & Yaari, Menahem E, 1970. "Markets with Countably Many Commodities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 369-77, October.
  12. Karni, Edi & Levin, Dan, 1994. "Social Attributes and Strategic Equilibrium: A Restaurant Pricing Game," Journal of Political Economy, University of Chicago Press, vol. 102(4), pages 822-40, August.
  13. Karni, Edi & Schmeidler, David, 1990. "Fixed Preferences and Changing Tastes," American Economic Review, American Economic Association, vol. 80(2), pages 262-67, May.
  14. Aumann, Robert J., 1976. "An elementary proof that integration preserves uppersemicontinuity," Journal of Mathematical Economics, Elsevier, vol. 3(1), pages 15-18, March.
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