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p-Best response set

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  • Tercieux, Olivier

Abstract

This paper introduces a notion of p-best response set (p-BR). We build on this notion in order to provide a new set-valued concept: the minimal p-best response set (p-MBR). After proving general existence results of the p-MBR, we show that it characterizes set-valued stability concepts in a dynamic with Poisson revision opportunities borrowed from Matsui and Matsuyama [An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415-434.] Then, we study equilibrium selection. In particular, using our notion of p-BR, we generalize Morris et al. [p-Dominance and belief potential, Econometrica 63 (1995) 145-157.] that aimed to provide sufficient conditions under which a unique equilibrium is selected in the presence of higher order uncertainty.
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  • Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
  • Handle: RePEc:eee:jetheo:v:131:y:2006:i:1:p:45-70
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    References listed on IDEAS

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    1. 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, January.
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    8. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
    9. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136 World Scientific Publishing Co. Pte. Ltd..
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    15. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
    16. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    17. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October.
    18. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, vol. 107(2), pages 288-310, December.
    19. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
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    Citations

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    Cited by:

    1. UNO, Hiroshi, 2011. "Nested potentials and robust equilibria," CORE Discussion Papers 2011009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
    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.
    4. John Duggan & Michel Le Breton, 2014. "Choice-theoretic Solutions for Strategic Form Games," RCER Working Papers 580, University of Rochester - Center for Economic Research (RCER).
    5. Andrea Gallice, 2013. "Equilibrium selection through pu-dominance," Carlo Alberto Notebooks 327, Collegio Carlo Alberto.
    6. Olivier Tercieux & Vincent Vannetelbosch, 2006. "A characterization of stochastically stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 351-369, October.
    7. J. Durieu & P. Solal, 2014. "Local Interactions and p -Best Response Set," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-7, March.
    8. J. Durieu & P. Solal & O. Tercieux, 2011. "Adaptive learning and p-best response sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 735-747, November.
    9. Geir B. , Asheim & Voorneveld, Max & W. Weibull, Jörgen, 2009. "Epistemically Stable Strategy Sets," Memorandum 01/2010, Oslo University, Department of Economics.
    10. 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.
    11. Olivier Tercieux & Mark Voorneveld, 2010. "The cutting power of preparation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 85-101, February.
    12. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    13. Kojima, Fuhito & Takahashi, Satoru, 2008. "p-Dominance and perfect foresight dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 689-701, September.
    14. repec:spr:compst:v:71:y:2010:i:1:p:85-101 is not listed on IDEAS
    15. 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.
    16. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    17. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-16, November.
    18. Oyama, Daisuke & Sandholm, William H. & Tercieux, Olivier, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    19. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.
    20. Iijima, Ryota, 2015. "Iterated generalized half-dominance and global game selection," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 120-136.

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