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Generalized risk-dominance and asymmetric dynamics

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  • Peski, Marcin

Abstract

This paper proposes two (ordinal and cardinal) generalizations of [J.C. Harsanyi, R. Selten, A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge, MA and London, 1988] risk-dominance to multi-player, multi-action games. There are three reasons why generalized risk-dominance (GR-dominance) is interesting. Extending the logic of risk-dominance, GR-dominant actions can be interpreted as best responses to conjectures that satisfy a certain type of symmetry. Second, in a local interaction game of [G. Ellison, Learning, local interaction, and coordination, Econometrica 61 (5) (1993) 1047], if an action is risk-dominant in individual binary interactions with neighbors, it is also GR-dominant in the large game on a network. Finally, we show that GR-dominant actions are stochastically stable under a class of evolutionary dynamics. The last observation is a corollary to new abstract selection results that applies to a wide class of so-called asymmetric dynamics. In particular, I show that a (strictly) ordinal GR-dominant profile is (uniquely) stochastically stable under the approximate best-response dynamics of [M. Kandori, G.J. Mailath, R. Rob, Learning, mutation, and long run equilibria in games, Econometrica 61 (1) (1993) 29]. A (strictly) cardinal GR-dominant equilibrium is (uniquely) stochastically stable under a class of payoff-based dynamics that includes [L.E. Blume, The statistical-mechanics of strategic interaction, Games Econ. Behav. 5 (3) (1993) 387-424]. Among others, this leads to a generalization of a result from [G. Ellison, Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution, Rev. Econ. Stud. 67 (230) (2000) 17] on the -dominant evolutionary selection to all networks and the unique selection to all networks that satisfy a simple, sufficient condition.

Suggested Citation

  • Peski, Marcin, 2010. "Generalized risk-dominance and asymmetric dynamics," Journal of Economic Theory, Elsevier, vol. 145(1), pages 216-248, January.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:216-248
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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.
    2. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    3. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 17-45.
    4. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    5. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    6. 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.
    7. Lee In Ho & Szeidl Adam & Valentinyi Akos, 2003. "Contagion and State Dependent Mutations," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-29, February.
    8. Jackson, Matthew O. & Watts, Alison, 2002. "On the formation of interaction networks in social coordination games," Games and Economic Behavior, Elsevier, vol. 41(2), pages 265-291, November.
    9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    10. Andreas Blume & Ted Temzelides, 2003. "On the geography of conventions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 863-873, November.
    11. Noldeke Georg & Samuelson Larry, 1993. "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 425-454, July.
    12. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
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    Citations

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    Cited by:

    1. Gary Charness & Francesco Feri & Miguel A. Meléndez‐Jiménez & Matthias Sutter, 2014. "Experimental Games on Networks: Underpinnings of Behavior and Equilibrium Selection," Econometrica, Econometric Society, vol. 82, pages 1615-1670, September.
    2. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    3. Kamm, Aaron & Koch, Christian & Nikiforakis, Nikos, 2017. "The ghost of institutions past: History as an obstacle to fighting tax evasion," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168271, Verein für Socialpolitik / German Economic Association.
    4. repec:spr:joecth:v:64:y:2017:i:3:d:10.1007_s00199-016-0988-x is not listed on IDEAS
    5. Iijima, Ryota, 2015. "Iterated generalized half-dominance and global game selection," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 120-136.
    6. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," LSE Research Online Documents on Economics 65422, London School of Economics and Political Science, LSE Library.
    7. Newton, Jonathan & Angus, Simon D., 2015. "Coalitions, tipping points and the speed of evolution," Journal of Economic Theory, Elsevier, vol. 157(C), pages 172-187.
    8. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.
    9. Christopher Kah & Markus Walzl, 2015. "Stochastic Stability in a Learning Dynamic with Best Response to Noisy Play," Working Papers 2015-15, Faculty of Economics and Statistics, University of Innsbruck.
    10. Ennio Bilancini & Leonardo Boncinelli, 2015. "Social coordination with locally observable types," Department of Economics 0051, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    11. Heggedal, Tom-Reiel & Helland, Leif, 2014. "Platform selection in the lab," Journal of Economic Behavior & Organization, Elsevier, vol. 99(C), pages 168-177.
    12. Syngjoo Choi & Edoardo Gallo & Shachar Kariv, 2015. "Networks in the laboratory," Cambridge Working Papers in Economics 1551, Faculty of Economics, University of Cambridge.
    13. Neary, Philip R., 2012. "Competing conventions," Games and Economic Behavior, Elsevier, vol. 76(1), pages 301-328.
    14. Newton, Jonathan & Wait, Andrew & Angus, Simon D., 2016. "Watercooler chat, organizational structure and corporate culture," Working Papers 2016-03, University of Sydney, School of Economics.
    15. Willington Manuel & Alegría Alexander, 2012. "Collusion in a One-Period Insurance Market with Adverse Selection," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-32, April.
    16. Sung-Ha Hwang & Jonathan Newton, 2017. "Payoff-dependent dynamics and coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 589-604, October.
    17. repec:jmi:articl:jmi-v2i1a5 is not listed on IDEAS
    18. Ennio Bilancini & Leonardo Boncinelli, 2014. "Social coordination with locally observable types," Center for Economic Research (RECent) 108, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    19. Man, Priscilla T.Y., 2012. "Efficiency and stochastic stability in normal form games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 272-284.

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