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Iterated Potential and Robustness of Equilibria

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  • Oyama, Daisuke
  • Tercieux, Olivier

Abstract

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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Bibliographic Info

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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Keywords: equilibrium selection; robustness; incomplete information; perfect foresight dynamics; iteration; monotone potential; p-dominance;

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References

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  1. Dirk Bergemann & Stephen Morris, 2007. "The Role of the Common Prior in Robust Implementation," Levine's Bibliography 122247000000001574, UCLA Department of Economics.
  2. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Departmental Working Papers, Rutgers University, Department of Economics 200807, Rutgers University, Department of Economics.
  3. Carlsson, H. & Damme, E.E.C. van, 1993. "Global games and equilibrium selection," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154416, Tilburg University.
  4. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  5. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Wiley Blackwell, Wiley Blackwell, vol. 42(1), pages 45-61, March.
  6. Matsuyama, Kiminori, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 106(2), pages 617-50, May.
  7. Josef Hofbauer & Daisuke Oyama & Satoru Takahashi, 2004. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Econometric Society 2004 North American Winter Meetings, Econometric Society 339, Econometric Society.
  8. 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.
  9. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Levine's Working Paper Archive 506439000000000325, David K. Levine.
  10. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  13. Tercieux, Olivier, 2006. "p-Best response set and the robustness of equilibria to incomplete information," Games and Economic Behavior, Elsevier, Elsevier, vol. 56(2), pages 371-384, August.
  14. Akihiko Matsui & Kiminori Matsuyama, 1991. "An Approach to Equilibrium Selection," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1065, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  16. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers, Penn Economics Department ed504c985fc375cbe719b3f60, Penn Economics Department.
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  20. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 39(6), pages 696-713, November.
  21. Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, Elsevier, vol. 132(1), pages 367-382, January.
  22. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, Elsevier, vol. 56(2), pages 299-322, August.
  23. Morris, S & Song Shin, H, 1996. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," Economics Papers 126, Economics Group, Nuffield College, University of Oxford.
  24. Michihiro Kandori & Rafael Rob, 1997. "Bandwagon effects and long run technology choice," Levine's Working Paper Archive 1265, David K. Levine.
  25. Kojima, Fuhito, 2006. "Risk-dominance and perfect foresight dynamics in N-player games," Journal of Economic Theory, Elsevier, Elsevier, vol. 128(1), pages 255-273, May.
  26. Hofbauer, Josef & Sorger, Gerhard, 1999. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Journal of Economic Theory, Elsevier, Elsevier, vol. 85(1), pages 1-23, March.
  27. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 57-84, January.
  28. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, Elsevier, vol. 107(2), pages 288-310, December.
  29. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 124-143, May.
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Citations

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Cited by:
  1. Oury, Marion, 2013. "Noise-independent selection in multidimensional global games," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(6), pages 2638-2665.
  2. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
  3. Daisuke Oyama & Olivier Tercieux, 2007. "Robust Equilibria under Non-Common Priors," Levine's Bibliography 843644000000000210, UCLA Department of Economics.
  4. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 39(6), pages 696-713, November.
  5. Nora, Vladyslav & Uno, Hiroshi, 2014. "Saddle functions and robust sets of equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 150(C), pages 866-877.
  6. Hiroshi Uno, 2007. "Nested Potential Games," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
  7. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Departmental Working Papers, Rutgers University, Department of Economics 200807, Rutgers University, Department of Economics.
  8. Christian Basteck & Tijmen R. Daniëls & Frank Heinemann, 2010. "Characterising Equilibrium Selection in Global Games with Strategic Complementarities," SFB 649 Discussion Papers SFB649DP2010-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Uno, Hiroshi, 2011. "Strategic complementarities and nested potential games," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 728-732.
  10. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 0. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, Econometric Society.
  11. Oyama, Daisuke & Takahashi, Satoru, 2011. "On the relationship between robustness to incomplete information and noise-independent selection in global games," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 683-688.
  12. Marion Oury, 2012. "Noise-Independent Selection in Multidimensional Global Games," THEMA Working Papers 2012-28, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  13. Daisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2011. "Perfect foresight dynamics in binary supermodular games," International Journal of Economic Theory, The International Society for Economic Theory, The International Society for Economic Theory, vol. 7(3), pages 251-267, 09.
  14. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
  15. UNO, Hiroshi, 2011. "Nested potentials and robust equilibria," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2011009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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