Two-Person Adversarial Games are Zero-Sum: An elaboration of a folk theorem
Mohammed Ali Khan, Arthur Paul Pedersen, David Schrittesser · Economics Letters · 2024
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.