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Iterated Potential and Robustness of Equilibria

Listed author(s):
  • 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: https://mpra.ub.uni-muenchen.de/1599/1/MPRA_paper_1599.pdf
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File URL: https://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
Handle: RePEc:pra:mprapa:1599
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  2. Michihiro, Kandori & Rob, Rafael, 1998. "Bandwagon Effects and Long Run Technology Choice," Games and Economic Behavior, Elsevier, vol. 22(1), pages 30-60, January.
  3. Oyama, Daisuke & Takahashi, Satoru & Hofbauer, Josef, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.
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  7. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
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  10. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
  11. 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.
  12. 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.
  13. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  14. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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  19. 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.
  20. Hofbauer, Josef & Sorger, Gerhard, 1999. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 1-23, March.
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  22. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  23. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
  24. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-1380, September.
  25. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
  26. Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 367-382, January.
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  29. Kim, Youngse, 1996. "Equilibrium Selection inn-Person Coordination Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 203-227, August.
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