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: Kouki Tsuji, Kenta Takashima, Yuzuru Sato, Takuma Akimoto
Format: Article
Language:English
Published: Springer 2025-06-01
Series:Discover Artificial Intelligence
Online Access:https://doi.org/10.1007/s44163-025-00283-z
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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
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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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