Universality in game-driven random walks with strategies generated by a genetic algorithm
Abstract We investigate random walks driven by an asymmetric dual-choice game inspired by the rock-paper-scissors game. In this game, Player A selects either paper or scissors, while Player B chooses either rock or scissors. The random walk is generated by the game’s outcomes: a player advances by +...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer
2025-06-01
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| Series: | Discover Artificial Intelligence |
| Online Access: | https://doi.org/10.1007/s44163-025-00283-z |
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| _version_ | 1849725112077516800 |
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| author | Kouki Tsuji Kenta Takashima Yuzuru Sato Takuma Akimoto |
| author_facet | Kouki Tsuji Kenta Takashima Yuzuru Sato Takuma Akimoto |
| author_sort | Kouki Tsuji |
| collection | DOAJ |
| description | Abstract We investigate random walks driven by an asymmetric dual-choice game inspired by the rock-paper-scissors game. In this game, Player A selects either paper or scissors, while Player B chooses either rock or scissors. The random walk is generated by the game’s outcomes: a player advances by + 1 step upon winning, while the opponent regresses by − 1 step. Each player follows a strategy categorized as either a mixed strategy or an adaptive strategy optimized via a genetic algorithm (GA) that analyzes the opponent’s past hands. According to game theory, this game possesses a mixed strategy Nash equilibrium. We show that the game-driven random walk exhibits a biased random walk with correlated steps when one player employs a GA-based strategy and the opponent follows a mixed strategy. We find that when the opponent plays according to the probabilities at the Nash equilibrium, the step correlations disappear. These findings highlight the interplay between strategic adaptation and Nash equilibrium in game-driven random walks. |
| format | Article |
| id | doaj-art-35b7e7f4a7804d39b510134668819f5d |
| institution | DOAJ |
| issn | 2731-0809 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Springer |
| record_format | Article |
| series | Discover Artificial Intelligence |
| spelling | doaj-art-35b7e7f4a7804d39b510134668819f5d2025-08-20T03:10:34ZengSpringerDiscover Artificial Intelligence2731-08092025-06-015111310.1007/s44163-025-00283-zUniversality in game-driven random walks with strategies generated by a genetic algorithmKouki Tsuji0Kenta Takashima1Yuzuru Sato2Takuma Akimoto3Department of Physics, Tokyo University of ScienceDepartment of Physics, Tokyo University of ScienceRIES/Department of Mathematics, Hokkaido UniversityDepartment of Physics, Tokyo University of ScienceAbstract We investigate random walks driven by an asymmetric dual-choice game inspired by the rock-paper-scissors game. In this game, Player A selects either paper or scissors, while Player B chooses either rock or scissors. The random walk is generated by the game’s outcomes: a player advances by + 1 step upon winning, while the opponent regresses by − 1 step. Each player follows a strategy categorized as either a mixed strategy or an adaptive strategy optimized via a genetic algorithm (GA) that analyzes the opponent’s past hands. According to game theory, this game possesses a mixed strategy Nash equilibrium. We show that the game-driven random walk exhibits a biased random walk with correlated steps when one player employs a GA-based strategy and the opponent follows a mixed strategy. We find that when the opponent plays according to the probabilities at the Nash equilibrium, the step correlations disappear. These findings highlight the interplay between strategic adaptation and Nash equilibrium in game-driven random walks.https://doi.org/10.1007/s44163-025-00283-z |
| spellingShingle | Kouki Tsuji Kenta Takashima Yuzuru Sato Takuma Akimoto Universality in game-driven random walks with strategies generated by a genetic algorithm Discover Artificial Intelligence |
| title | Universality in game-driven random walks with strategies generated by a genetic algorithm |
| title_full | Universality in game-driven random walks with strategies generated by a genetic algorithm |
| title_fullStr | Universality in game-driven random walks with strategies generated by a genetic algorithm |
| title_full_unstemmed | Universality in game-driven random walks with strategies generated by a genetic algorithm |
| title_short | Universality in game-driven random walks with strategies generated by a genetic algorithm |
| title_sort | universality in game driven random walks with strategies generated by a genetic algorithm |
| url | https://doi.org/10.1007/s44163-025-00283-z |
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