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Two-Person Adversarial Games are Zero-Sum: An elaboration of a folk theorem

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  • Khan, M. Ali
  • Pedersen, Arthur Paul
  • Schrittesser, David

Abstract

The observation that every two-person adversarial game is an affine transformation of a zero-sum game is traceable to Luce and Raiffa (1957) and made explicit in Aumann (1987). Recent work of Adler et al. (2009) and of Raimondo (2023) in increasing generality, proves what has so far remained a conjecture. We present two proofs of an even more general formulation: the first draws on multilinear utility theory developed by Fishburn and Roberts (1978); the second is a consequence of Adler et al.’s 2009 proof itself for a special case of a two-player game in which each player has a set of three actions.

Suggested Citation

  • Khan, M. Ali & Pedersen, Arthur Paul & Schrittesser, David, 2024. "Two-Person Adversarial Games are Zero-Sum: An elaboration of a folk theorem," Economics Letters, Elsevier, vol. 242(C).
    • Handle: RePEc:eee:ecolet:v:242:y:2024:i:c:s0165176524003367
    DOI: 10.1016/j.econlet.2024.111852
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    References listed on IDEAS

    as
    1. Raimondo, Roberto, 2023. "Strictly competitive games with infinitely many strategies," Economics Letters, Elsevier, vol. 233(C).
    2. MOULIN, Hervé & VIAL, Jean-Philippe, 1978. "Strategically zero-sum games: the class of games whose completely mixed equilibria connot be improved upon," LIDAM Reprints CORE 359, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    More about this item

    Keywords

    Game Theory; Two-person Games; Strictly Competitive Games; Adversarial Games; Utility Theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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