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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. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 387-430, 06.
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  4. 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.
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  6. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
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  8. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(2), pages 223-227.
  9. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  10. 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.
  11. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  12. 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.
  13. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
  14. 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.
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