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Two-Person Adversarial Games are Zero-Sum: An Elaboration of a Folk Theorem

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

Abstract

The observation that every two-person adversarial game is an affine transformation of a zero-sum game is traceable to Luce & Raiffa (1957) and made explicit in Aumann (1987). Recent work of (ADP) 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 & Roberts (1978); the second is a consequence of the ADP proof itself for a special case of a two-player game with a set of three actions.

Suggested Citation

  • M. Ali Khan & Arthur Paul Pedersen & David Schrittesser, 2024. "Two-Person Adversarial Games are Zero-Sum: An Elaboration of a Folk Theorem," Papers 2403.04029, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2403.04029
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    References listed on IDEAS

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    5. Raimondo, Roberto, 2023. "Strictly competitive games with infinitely many strategies," Economics Letters, Elsevier, vol. 233(C).
    6. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759, Elsevier.
    7. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808, Elsevier.
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    More about this item

    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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