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Generalized risk-dominance and asymmetric dynamics

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  • Peski, Marcin
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 145 (2010)
    Issue (Month): 1 (January)
    Pages: 216-248

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    Handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:216-248

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    Web page: http://www.elsevier.com/locate/inca/622869

    Related research

    Keywords: Evolutionary theory Stochastic games;

    References

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    1. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    2. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
    3. 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.
    4. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
    5. 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.
    6. Hans Carlsson & Eric van Damme, 1993. "Global Games and Equilibrium Selection," Levine's Working Paper Archive 122247000000001088, David K. Levine.
    7. Ted Temzelides, 2000. "On the Geography of Conventions," Econometric Society World Congress 2000 Contributed Papers 0117, Econometric Society.
    8. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
    9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    10. 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.
    11. Adam Szeidl & In Ho Lee & Akos Valentinyi, 2001. "Contagion and State Dependent Mutations," IEHAS Discussion Papers 0104, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
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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," Working Papers 2014-14, Faculty of Economics and Statistics, University of Innsbruck.
    2. Neary, Philip R., 2012. "Competing conventions," Games and Economic Behavior, Elsevier, vol. 76(1), pages 301-328.
    3. 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.
    4. Heggedal, Tom-Reiel & Helland, Leif, 2014. "Platform selection in the lab," Journal of Economic Behavior & Organization, Elsevier, vol. 99(C), pages 168-177.
    5. Charness, Gary & Feri, Francesco & Meléndez-Jiménez, Miguel A. & Sutter, Matthias, 2014. "Experimental Games on Networks: Underpinnings of Behavior and Equilibrium Selection," IZA Discussion Papers 8104, Institute for the Study of Labor (IZA).

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