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Optimal strategy of the simultaneous dice game Pig for multiplayers: when reinforcement learning meets game theory
In this work, we focus on using reinforcement learning and game theory to solve for the optimal strategies for the dice game Pig, in a novel simultaneous playing setting. First, we derived analytically the optimal strategy for the 2-player simultaneous game using dynamic programming, mixed-strategy...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10199029/ https://www.ncbi.nlm.nih.gov/pubmed/37208437 http://dx.doi.org/10.1038/s41598-023-35237-x |
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author | Zhu, Tian Ma, Merry Chen, Lu Liu, Zhenhua |
author_facet | Zhu, Tian Ma, Merry Chen, Lu Liu, Zhenhua |
author_sort | Zhu, Tian |
collection | PubMed |
description | In this work, we focus on using reinforcement learning and game theory to solve for the optimal strategies for the dice game Pig, in a novel simultaneous playing setting. First, we derived analytically the optimal strategy for the 2-player simultaneous game using dynamic programming, mixed-strategy Nash equilibrium. At the same time, we proposed a new Stackelberg value iteration framework to approximate the near-optimal pure strategy. Next, we developed the corresponding optimal strategy for the multiplayer independent strategy game numerically. Finally, we presented the Nash equilibrium for simultaneous Pig game with infinite number of players. To help promote the learning of and interest in reinforcement learning, game theory and statistics, we have further implemented a website where users can play both the sequential and simultaneous Pig game against the optimal strategies derived in this work. |
format | Online Article Text |
id | pubmed-10199029 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-101990292023-05-21 Optimal strategy of the simultaneous dice game Pig for multiplayers: when reinforcement learning meets game theory Zhu, Tian Ma, Merry Chen, Lu Liu, Zhenhua Sci Rep Article In this work, we focus on using reinforcement learning and game theory to solve for the optimal strategies for the dice game Pig, in a novel simultaneous playing setting. First, we derived analytically the optimal strategy for the 2-player simultaneous game using dynamic programming, mixed-strategy Nash equilibrium. At the same time, we proposed a new Stackelberg value iteration framework to approximate the near-optimal pure strategy. Next, we developed the corresponding optimal strategy for the multiplayer independent strategy game numerically. Finally, we presented the Nash equilibrium for simultaneous Pig game with infinite number of players. To help promote the learning of and interest in reinforcement learning, game theory and statistics, we have further implemented a website where users can play both the sequential and simultaneous Pig game against the optimal strategies derived in this work. Nature Publishing Group UK 2023-05-19 /pmc/articles/PMC10199029/ /pubmed/37208437 http://dx.doi.org/10.1038/s41598-023-35237-x Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Zhu, Tian Ma, Merry Chen, Lu Liu, Zhenhua Optimal strategy of the simultaneous dice game Pig for multiplayers: when reinforcement learning meets game theory |
title | Optimal strategy of the simultaneous dice game Pig for multiplayers: when reinforcement learning meets game theory |
title_full | Optimal strategy of the simultaneous dice game Pig for multiplayers: when reinforcement learning meets game theory |
title_fullStr | Optimal strategy of the simultaneous dice game Pig for multiplayers: when reinforcement learning meets game theory |
title_full_unstemmed | Optimal strategy of the simultaneous dice game Pig for multiplayers: when reinforcement learning meets game theory |
title_short | Optimal strategy of the simultaneous dice game Pig for multiplayers: when reinforcement learning meets game theory |
title_sort | optimal strategy of the simultaneous dice game pig for multiplayers: when reinforcement learning meets game theory |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10199029/ https://www.ncbi.nlm.nih.gov/pubmed/37208437 http://dx.doi.org/10.1038/s41598-023-35237-x |
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