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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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    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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