Zero-determinant strategies in iterated multi-strategy games
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arXiv
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| Format: | Preprint |
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2014
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| _version_ | 1866917829913083904 |
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| author | Guo, Jin-Li |
| author_facet | Guo, Jin-Li |
| contents | Self-serving, rational agents sometimes cooperate to their mutual benefit. The two-player iterated prisoner's dilemma game is a model for including the emergence of cooperation. It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants. The recent discovery of the powerful class of zero-determinant strategies in the iterated prisoner's dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents. However, strategies in the prisoner's dilemma game are only two strategies. Are there these results for general multi-strategy games? To address this question, the paper develops a theory for zero-determinant strategies for multi-strategy games, with any number of strategies. The analytical results exhibit a similar yet different scenario to the case of two-strategy games. Zero-determinant strategies in iterated prisoner's dilemma can be seen as degenerate case of our results. The results are also applied to the snowdrift game, the hawk-dove game and the chicken game. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1409_1786 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Zero-determinant strategies in iterated multi-strategy games Guo, Jin-Li Computer Science and Game Theory General Economics Economics Physics and Society Self-serving, rational agents sometimes cooperate to their mutual benefit. The two-player iterated prisoner's dilemma game is a model for including the emergence of cooperation. It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants. The recent discovery of the powerful class of zero-determinant strategies in the iterated prisoner's dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents. However, strategies in the prisoner's dilemma game are only two strategies. Are there these results for general multi-strategy games? To address this question, the paper develops a theory for zero-determinant strategies for multi-strategy games, with any number of strategies. The analytical results exhibit a similar yet different scenario to the case of two-strategy games. Zero-determinant strategies in iterated prisoner's dilemma can be seen as degenerate case of our results. The results are also applied to the snowdrift game, the hawk-dove game and the chicken game. |
| title | Zero-determinant strategies in iterated multi-strategy games |
| topic | Computer Science and Game Theory General Economics Economics Physics and Society |
| url | https://arxiv.org/abs/1409.1786 |