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Best Response Equivalence

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Author Info
Morris, Stephen Morris (Cowles Foundation, Yale University)
Takashi Ui (Yokohama National University)

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Abstract

Two games are best-response equivalent if they have the same best-response correspondence. We provide a characterization of when two games are best-response equivalent. The characterizations exploit a dual relationship between payoff differences and beliefs. Some "potential game" arguments (cf. Monderer and Shapley, 1996, Games. Econ. Behav. 14, 124-143) rely only on the property that potential games are best-response equivalent to identical interest games. Our results show that a large class of games are best-response equivalent to identical interest games, but are not potential games. Thus we show how some existing potential game arguments can be extended.

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File URL: http://cowles.econ.yale.edu/P/cd/d13b/d1377.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1377.

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Length: 31 pages
Date of creation: Jul 2002
Date of revision:
Publication status: Published in Games and Economic Behavior (2004), 49: 260-287
Handle: RePEc:cwl:cwldpp:1377

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Best response equivalence; Duality; Farkas' Lemma; Potential games;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  2. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March. [Downloadable!] (restricted)
  3. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April. [Downloadable!] (restricted)
  4. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Cowles Foundation Discussion Papers 1394, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  5. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Brock, William A & Durlauf, Steven N, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Blackwell Publishing, vol. 68(2), pages 235-60, April.
  9. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer, vol. 32(3), pages 387-430, 06. [Downloadable!] (restricted)
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  10. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer, vol. 26(2), pages 223-227.
  11. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January. [Downloadable!] (restricted)
  12. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)
  13. P. Dubey, O. Haimanko, A. Zapechelnyuk, 2002. "Strategic Substitutes and Potential Games," Department of Economics Working Papers 02-02, Stony Brook University, Department of Economics. [Downloadable!]
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Tercieux, Olivier & Voorneveld, Mark, 2005. "The cutting power of preparation," Discussion Paper 94, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  2. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Cowles Foundation Discussion Papers 1394, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Levine's Bibliography 122247000000001569, UCLA Department of Economics. [Downloadable!]
    Other versions:
  4. V. Bhaskar & George J. Mailath & Stephen Morris, 2009. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," PIER Working Paper Archive 09-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
    Other versions:
  5. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2007. "Ordinal Games," Economics working paper series 07/74, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
  6. Hiroshi Uno, 2007. "Nested Potential Games," Economics Bulletin, Economics Bulletin, vol. 3(19), pages 1-8. [Downloadable!]
  7. smorris & Takashi Ui, 2004. "Generalized Potentials and Robust Sets of Equilibria," Econometric Society 2004 North American Winter Meetings 45, Econometric Society. [Downloadable!]
  8. Nikolai S. Kukushkin, 2008. "Potential games with NM utilities," Economics Bulletin, Economics Bulletin, vol. 3(17), pages 1-7. [Downloadable!]
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