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The Robust Nash Equilibrium and Equilibrium Selection in 2x2 Coordination Games

Author

Listed:
  • Raul V. Fabella

    (University of the Philippines School of Economics)

  • Vigile Marie B. Fabella

    (Universitët Konstanz, Germany)

Abstract

We propose an equilibrium concept, the Robust Nash equilibrium (RNE), that combines the best-reply rationality and the "first mover invariance" condition. The single-stage 2x2 symmetric information game G is transformed into sequential two-stage games with two sub-trees: STA has the row player starting and STB has the column player starting. A profile in G is robust if it is the strict SPNE of the two branches; it is ephemeral if it is not the SPNE of any branch. We show that every strict dominant strategy equilibrium of G is robust but not every strict Nash equilibrium of G is. We show further that every robust profile of G is always a strict Nash equilibrium of G. A Robust Nash equilibrium (RNE) of G is any robust profile of G. The RNE of G is unique. We show in particular that the payoff dominant strict Nash equilibrium of a coordination game G is RNE while the strictly payoff-dominated Nash equilibrium of G is ephemeral. The original Harsanyi-Selten preference for payoff dominance over risk dominance is supported by robustness without invoking collective rationality.

Suggested Citation

  • Raul V. Fabella & Vigile Marie B. Fabella, 2012. "The Robust Nash Equilibrium and Equilibrium Selection in 2x2 Coordination Games," UP School of Economics Discussion Papers 201216, University of the Philippines School of Economics.
    • Handle: RePEc:phs:dpaper:201216
    as

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    File URL: https://pre.econ.upd.edu.ph/upsedp/index.php/dp/article/view/699
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    References listed on IDEAS

    as
    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, December.
    2. Harsanyi John C., 1995. "A New Theory of Equilibrium Selection for Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 10(2), pages 318-332, August.
    3. George A. Akerlof & Rachel E. Kranton, 2005. "Identity and the Economics of Organizations," Journal of Economic Perspectives, American Economic Association, vol. 19(1), pages 9-32, Winter.
    4. Burdzy, Krzysztof & Frankel, David M & Pauzner, Ady, 2001. "Fast Equilibrium Selection by Rational Players Living in a Changing World," Econometrica, Econometric Society, vol. 69(1), pages 163-189, January.
    5. Eckel, Catherine C. & Grossman, Philip J., 2005. "Managing diversity by creating team identity," Journal of Economic Behavior & Organization, Elsevier, vol. 58(3), pages 371-392, November.
    6. Basu, Kaushik, 2006. "Participatory Equity, Identity, and Productivity: Policy Implications for Promoting Development," Working Papers 06-06, Cornell University, Center for Analytic Economics.
    7. Kim, Youngse, 1996. "Equilibrium Selection inn-Person Coordination Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 203-227, August.
    8. Carlsson, H. & van Damme, E.E.C., 1991. "Equilibrium selection in stag hunt games," Discussion Paper 1991-70, Tilburg University, Center for Economic Research.
    9. 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.
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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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