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Best response equivalence

  • Morris, Stephen
  • Ui, Takashi

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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 49 (2004)
Issue (Month): 2 (November)
Pages: 260-287

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Handle: RePEc:eee:gamebe:v:49:y:2004:i:2:p:260-287
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Cowles Foundation Discussion Papers 1394, Cowles Foundation for Research in Economics, Yale University.
  2. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  3. 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.
  4. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer, vol. 32(3), pages 387-430, 06.
  5. Brock,W.A. & Durlauf,S.N., 2000. "Discrete choice with social interactions," Working papers 7, Wisconsin Madison - Social Systems.
  6. 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.
  7. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
  8. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
  9. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  10. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer, vol. 26(2), pages 223-227.
  11. 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.
  12. Eric Maskin & Jean Tirole, 1997. "Markov Perfect Equilibrium, I: Observable Actions," Harvard Institute of Economic Research Working Papers 1799, Harvard - Institute of Economic Research.
  13. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  14. 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.
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