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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
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    File URL: http://www.econ.upd.edu.ph/dp/index.php/dp/article/view/699
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Nash Equilibrium;

    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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