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Iterated Potential and Robustness of Equilibria

  • Oyama, Daisuke
  • Tercieux, Olivier

For any given set-valued solution concept, it is possible to consider iterative elimination of actions outside the solution set. This paper applies such a procedure to define the concept of iterated monotone potential maximizer (iterated MP-maximizer). It is shown that under some monotonicity conditions, an iterated MP-maximizer is robust to incomplete information (Kajii and Morris, Econometrica 65 (1997)) and absorbing and globally accessible under perfect foresight dynamics for a small friction (Matsui and Matsuyama, Journal of Economic Theory 65 (1995)). Several simple sufficient conditions under which a game has an iterated MP-maximizer are also provided.

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File URL: http://mpra.ub.uni-muenchen.de/14320/1/MPRA_paper_14320.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 1599.

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Date of creation: 31 Dec 2004
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Handle: RePEc:pra:mprapa:1599
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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. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
  3. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, vol. 107(2), pages 288-310, December.
  4. Dirk Bergemann & Stephen Morris, 2008. "The Role of the Common Prior in Robust Implementation," Journal of the European Economic Association, MIT Press, vol. 6(2-3), pages 551-559, 04-05.
  5. Michihiro Kandori & Rafael Rob, 1997. "Bandwagon effects and long run technology choice," Levine's Working Paper Archive 1265, David K. Levine.
  6. Josef HOFBAUER & Gerhard SORGER, 1998. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Vienna Economics Papers vie9802, University of Vienna, Department of Economics.
  7. Hans Carlsson & Eric van Damme, 1993. "Global Games and Equilibrium Selection," Levine's Working Paper Archive 122247000000001088, David K. Levine.
  8. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  9. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 696-713, November.
  10. 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, June.
  11. Slade, M.E., 1989. "What Does An Oligopoly Maximize?," G.R.E.Q.A.M. 89a14, Universite Aix-Marseille III.
  12. S. Morris & R. Rob & H. Shin, 2010. "p-dominance and Belief Potential," Levine's Working Paper Archive 505, David K. Levine.
  13. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  14. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
  15. Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 367-382, January.
  16. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  18. Deisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Vienna Economics Papers 0318, University of Vienna, Department of Economics.
  19. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  20. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  21. Matsuyama, Kiminori, 1992. "A Simple Model of Sectoral Adjustment," Review of Economic Studies, Wiley Blackwell, vol. 59(2), pages 375-88, April.
  22. Morris, Stephen & Shin, Hyun Song, 1997. "Unique Equilibrium in a Model of Self-fulfilling Currency Attacks," CEPR Discussion Papers 1687, C.E.P.R. Discussion Papers.
  23. Matsuyama, Kiminori, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 617-50, May.
  24. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  25. Kim, Youngse, 1996. "Equilibrium Selection inn-Person Coordination Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 203-227, August.
  26. Tercieux, Olivier, 2006. "p-Best response set and the robustness of equilibria to incomplete information," Games and Economic Behavior, Elsevier, vol. 56(2), pages 371-384, August.
  27. Kojima, Fuhito, 2006. "Risk-dominance and perfect foresight dynamics in N-player games," Journal of Economic Theory, Elsevier, vol. 128(1), pages 255-273, May.
  28. Matsuyama, Kiminori, 1992. "The market size, entrepreneurship, and the big push," Journal of the Japanese and International Economies, Elsevier, vol. 6(4), pages 347-364, December.
  29. repec:ner:tilbur:urn:nbn:nl:ui:12-154416 is not listed on IDEAS
  30. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Economics Working Papers 0085, Institute for Advanced Study, School of Social Science.
  31. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
  32. Itay Goldstein & Ady Pauzner, 2005. "Demand-Deposit Contracts and the Probability of Bank Runs," Journal of Finance, American Finance Association, vol. 60(3), pages 1293-1327, 06.
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