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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.

Suggested Citation

  • Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:1599
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Oyama, Daisuke & Tercieux, Olivier, 2010. "Robust equilibria under non-common priors," Journal of Economic Theory, Elsevier, vol. 145(2), pages 752-784, March.
    2. Nora, Vladyslav & Uno, Hiroshi, 2014. "Saddle functions and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 150(C), pages 866-877.
    3. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
    4. Honda, Jun, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Paper Series 4582, WU Vienna University of Economics and Business.
    5. 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.
    6. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
    7. Kota Murayama, 2015. "Robust Predictions under Finite Depth of Reasoning," Discussion Paper Series DP2015-28, Research Institute for Economics & Business Administration, Kobe University.
    8. 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.
    9. UNO, Hiroshi, 2011. "Nested potentials and robust equilibria," CORE Discussion Papers 2011009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. 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, vol. 7(3), pages 251-267, September.
    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. Iijima, Ryota, 2015. "Iterated generalized half-dominance and global game selection," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 120-136.
    13. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    14. Okada, Daijiro & Tercieux, Olivier, 2012. "Log-linear dynamics and local potential," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1140-1164.
    15. Basteck, Christian & Daniëls, Tijmen R. & Heinemann, Frank, 2013. "Characterising equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2620-2637.
    16. Hiroshi Uno, 2007. "Nested Potential Games," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
    17. Uno, Hiroshi, 2011. "Strategic complementarities and nested potential games," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 728-732.
    18. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    19. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    20. Oury, Marion, 2013. "Noise-independent selection in multidimensional global games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2638-2665.

    More about this item

    Keywords

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

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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