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Finite approximations of the Sion-Wolfe game

Author

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  • Leopold Aspect
  • Christian Ewerhart

Abstract

As pointed out by Sion and Wolfe (1957), a non-cooperative game on the unit square need not admit a Nash equilibrium, neither in pure nor in randomized strategies. In this paper, we consider finite approximations of the Sion-Wolfe game. For all parameter constellations relevant for the limit consideration, we characterize the set of Nash equilibria in iteratively undominated strategies. Values of finite approximations of the Sion-Wolfe game are shown to accumulate around three values that do not correspond in a simple way to the majorant and minorant values of the continuous game. To understand why this is happening, we apply the iterated elimination of weakly dominated strategies to the continuous game as well. The existence of ε-equilibrium, however, does not seem to be related to the properties of finite approximations.

Suggested Citation

  • Leopold Aspect & Christian Ewerhart, 2022. "Finite approximations of the Sion-Wolfe game," ECON - Working Papers 417, Department of Economics - University of Zurich, revised Aug 2023.
    • Handle: RePEc:zur:econwp:417
    as

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    File URL: https://www.zora.uzh.ch/id/eprint/220546/7/econwp417.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Two-person zero-sum games; Sion-Wolfe game; existence of Nash equilibrium; finite approximations; iterated elimination of dominated strategies; ε-equilibrium; Colonel Blotto games;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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