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

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  • M Ali Khan
  • Kali P Rath
  • Yeneng Sun

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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Bibliographic Info

Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 381.

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Date of creation: Jan 1994
Date of revision: Feb 1997
Handle: RePEc:jhu:papers:381

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References

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  1. Masso, Jordi, 1993. "Undiscounted equilibrium payoffs of repeated games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 243-264.
  2. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
  3. 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.
  4. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
  5. Dubey, Pradeep & Mas-Colell, Andreau & Shubik, Martin, 1980. "Efficiency properties of strategies market games: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 22(2), pages 339-362, April.
  6. Aumann, Robert J., 1976. "An elementary proof that integration preserves uppersemicontinuity," Journal of Mathematical Economics, Elsevier, vol. 3(1), pages 15-18, March.
  7. James Bergin & Dan Bernhardt, 1989. "Anonymous Sequential Games with Aggregate Uncertainty," Working Papers 760, Queen's University, Department of Economics.
  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. 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.
  10. Karni, Edi & Schmeidler, David, 1990. "Fixed Preferences and Changing Tastes," American Economic Review, American Economic Association, vol. 80(2), pages 262-67, May.
  11. 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.
  12. 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.
  13. 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.
  14. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
  15. Constantinides, George M. & Rosenthal, Robert W., 1984. "Strategic analysis of the competitive exercise of certain financial options," Journal of Economic Theory, Elsevier, vol. 32(1), pages 128-138, February.
  16. 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.
  17. 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.
  18. Pascoa Mario Rui, 1993. "Noncooperative Equilibrium and Chamberlinian Monopolistic Competition," Journal of Economic Theory, Elsevier, vol. 60(2), pages 335-353, August.
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