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How Risky is it to Deviate from Nash Equilibrium?

Author

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  • Irit Nowik

    (Department of Industrial Engineering and Management, Lev Academic Center (JCT), 21 Havaad Haleumi, Jerusalem 91160, Israel)

Abstract

The purpose of this work is to offer for each player and any Nash equilibrium (NE), a measure for the potential risk in deviating from the NE strategy in any two person matrix game. We present two approaches regarding the nature of deviations: Strategic and Accidental. Accordingly, we define two models: S-model and T-model. The S-model defines a new game in which players deviate in the least dangerous direction. The risk defined in the T-model can serve as a refinement for the notion of “trembling hand perfect equilibrium†introduced by R. Selten. The risk measures enable testing and evaluating predictions on the behavior of players. For example: do players deviate more from a NE that is less risky? This may be relevant to the design of experiments. We present an Integer programming problem that computes the risk for any given player and NE. In the special case of zero-sum games with a unique strictly mixed NE, we prove that the risks of the players always coincide, even if the game is far from symmetry. This result holds for any norm we use for the size of deviations. We compare our risk measures to the risk measure defined by Harsanyi and Selten which is based on criteria of stability rather than on potential damage. We show that the measures may contradict.

Suggested Citation

  • Irit Nowik, 2016. "How Risky is it to Deviate from Nash Equilibrium?," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-24, September.
    • Handle: RePEc:wsi:igtrxx:v:18:y:2016:i:03:n:s0219198916500067
    DOI: 10.1142/S0219198916500067
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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, April.
    2. Maschler,Michael & Solan,Eilon & Zamir,Shmuel, 2013. "Game Theory," Cambridge Books, Cambridge University Press, number 9781107005488.
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