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Justifying optimal play via consistency

Author

Listed:
  • Brandl, Florian

    (Computer Science Department, Technische Universität München)

  • Brandt, Felix

    (Computer Science Department, Technische Universität München)

Abstract

Developing normative foundations for optimal play in two-player zero-sum games has turned out to be surprisingly difficult, despite the powerful strategic implications of the Minimax Theorem. We characterize maximin strategies by postulating coherent behavior in varying games. The first axiom, called consequentialism, states that how probability is distributed among completely indistinguishable actions is irrelevant. The second axiom, consistency, demands that strategies that are optimal in two different games should still be optimal when there is uncertainty which of the two games will actually be played. Finally, we impose a very mild rationality assumption, which merely requires that strictly dominated actions will not be played. Our characterization shows that a rational and consistent consequentialist who ascribes the same properties to his opponent has to play maximin strategies. This result can be extended to characterize Nash equilibrium in bimatrix games whenever the set of equilibria is interchangeable.

Suggested Citation

  • Brandl, Florian & Brandt, Felix, 2019. "Justifying optimal play via consistency," Theoretical Economics, Econometric Society, vol. 14(4), November.
    • Handle: RePEc:the:publsh:3423
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    References listed on IDEAS

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    Cited by:

    1. St'ephane Gonzalez & Nikolaos Pnevmatikos, 2023. "A Story of Consistency: Bridging the Gap between Bentham and Rawls Foundations," Papers 2303.07488, arXiv.org, revised Oct 2023.
    2. Fabien Gensbittel & Marcin Peski & Jérôme Renault, 2021. "Value-Based Distance Between Information Structures," Working Papers hal-01869139, HAL.
    3. Florian Brandl & Felix Brandt, 2023. "A Robust Characterization of Nash Equilibrium," Papers 2307.03079, arXiv.org, revised Jun 2024.
    4. Brandl, Florian & Brandt, Felix, 2024. "An axiomatic characterization of Nash equilibrium," Theoretical Economics, Econometric Society, vol. 19(4), November.

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    More about this item

    Keywords

    Zero-sum games; axiomatic characterization; maximin strategies;
    All these keywords.

    JEL classification:

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

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