Two-Person Adversarial Games are Zero-Sum: An Elaboration of a Folk Theorem
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913595596472320 |
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| author | Khan, M. Ali Pedersen, Arthur Paul Schrittesser, David |
| author_facet | Khan, M. Ali Pedersen, Arthur Paul Schrittesser, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04029 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-Person Adversarial Games are Zero-Sum: An Elaboration of a Folk Theorem Khan, M. Ali Pedersen, Arthur Paul Schrittesser, David Theoretical Economics 91A05, 91A10, 91A30 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. |
| title | Two-Person Adversarial Games are Zero-Sum: An Elaboration of a Folk Theorem |
| topic | Theoretical Economics 91A05, 91A10, 91A30 |
| url | https://arxiv.org/abs/2403.04029 |