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A Dynamic Homotopy Interpretation of Quantal Response Equilibrium Correspondences

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  • Theodore L. Turocy

    (Texas A&M University)

Abstract

This paper uses properties of the logistic quantal response equilibrium correspondence to compute Nash equilibria in nite games. It is shown that branches of the correspondence may be numerically traversed e ciently and securely. The method can be implemented on a multicomputer, allowing for application to large games. The path followed by the method has an interpretation analogous to Harsanyi and Selten's Tracing Procedure. As an application, it is shown that the principal branch of any quantal response equilibrium correspondence satisfying a monotonicity property converges to the risk-dominant equilibrium in 2x2 games.

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File URL: http://128.118.178.162/eps/game/papers/0212/0212001.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0212001.

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Length: 26 pages
Date of creation: 02 Dec 2002
Date of revision: 16 Oct 2003
Handle: RePEc:wpa:wuwpga:0212001

Note: Type of Document - PDF; prepared on Linux; pages: 26 ; figures: none
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Web page: http://128.118.178.162

Related research

Keywords: noncooperative games; computation of Nash equilibrium; quantal response; logit equilibrium.;

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  1. Jacob K. Goeree & Charles A. Holt & Thomas R. Palfrey, 2000. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Virginia Economics Online Papers 345, University of Virginia, Department of Economics.
  2. Roger B. Myerson, 1977. "Refinements of the Nash Equilibrium Concept," Discussion Papers 295, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Govindan, Srihari & Wilson, Robert, 2004. "Computing Nash equilibria by iterated polymatrix approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1229-1241, April.
  4. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  5. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  6. Ed Hopkins, 2004. "Two Competing Models of How People Learn in Games," ESE Discussion Papers 51, Edinburgh School of Economics, University of Edinburgh.
  7. Yamamoto, Yoshitsugu, 1993. "A Path-Following Procedure to Find a Proper Equilibrium of Finite Games," International Journal of Game Theory, Springer, vol. 22(3), pages 249-59.
  8. Anderson, Simon P. & Goeree, Jacob K. & Holt, Charles A., 2001. "Minimum-Effort Coordination Games: Stochastic Potential and Logit Equilibrium," Games and Economic Behavior, Elsevier, vol. 34(2), pages 177-199, February.
  9. Wilson, Robert, 1992. "Computing Simply Stable Equilibria," Econometrica, Econometric Society, vol. 60(5), pages 1039-70, September.
  10. Herings, P.J.J. & Elzen, A.H. van den, 1998. "Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games," Discussion Paper 1998-04, Tilburg University, Center for Economic Research.
  11. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  12. Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
  13. Thomas Palfrey, 2002. "Quantal Response Equilibrium and Overbidding in Private Value Auctions," Theory workshop papers 357966000000000089, UCLA Department of Economics.
  14. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
  15. Charles A. Holt & Jacob K. Goeree, 1999. "Stochastic Game Theory: For Playing Games, Not Just for Doing Theory," Virginia Economics Online Papers 306, University of Virginia, Department of Economics.
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