English

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

Theoretical Economics 2024-12-04 v5

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.

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Cite

@article{arxiv.2403.04029,
  title  = {Two-Person Adversarial Games are Zero-Sum: An Elaboration of a Folk Theorem},
  author = {M. Ali Khan and Arthur Paul Pedersen and David Schrittesser},
  journal= {arXiv preprint arXiv:2403.04029},
  year   = {2024}
}