Learning Strategic Value and Cooperation in Multi-Player Stochastic Games through Side Payments
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866918491219558400 |
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| author | Chen, Yixin Richley, Jeffrey Perez-Lavin, Darleen Syal, Jessica Singh Kia, Solmaz Kuhnle, Alan |
| author_facet | Chen, Yixin Richley, Jeffrey Perez-Lavin, Darleen Syal, Jessica Singh Kia, Solmaz Kuhnle, Alan |
| contents | We study general-sum, multi-player stochastic games with transferable utility, motivated by settings where agents can use side payments to make cooperation individually rational. Building on the Harsanyi--Shapley (HS) value for normal-form games, we introduce two HS-based value notions for stochastic games: HS-S, defined by aggregating dynamic coalition-versus-complement threat powers, and Coco-S, defined as fixed points of a statewise HS Bellman operator. We extend HS-style axioms to the stochastic setting and show that HS-S is the unique mapping satisfying them. We prove that HS-S and Coco-S coincide in all two-player stochastic games, but can disagree when $n>2$, via an explicit three-player counterexample. We prove existence and uniqueness of Coco-S fixed points for all two-player games and for three-player two-state games via topological degree theory, and provide an axiomatic characterization of Coco-S through a new \emph{Markov Consistency} axiom that distinguishes it from HS-S. Finally, we give sampling-based estimators with finite-sample guarantees and empirically compare the induced values, policies, and side payments on multi-player grid-game benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05307 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learning Strategic Value and Cooperation in Multi-Player Stochastic Games through Side Payments Chen, Yixin Richley, Jeffrey Perez-Lavin, Darleen Syal, Jessica Singh Kia, Solmaz Kuhnle, Alan Computer Science and Game Theory Artificial Intelligence We study general-sum, multi-player stochastic games with transferable utility, motivated by settings where agents can use side payments to make cooperation individually rational. Building on the Harsanyi--Shapley (HS) value for normal-form games, we introduce two HS-based value notions for stochastic games: HS-S, defined by aggregating dynamic coalition-versus-complement threat powers, and Coco-S, defined as fixed points of a statewise HS Bellman operator. We extend HS-style axioms to the stochastic setting and show that HS-S is the unique mapping satisfying them. We prove that HS-S and Coco-S coincide in all two-player stochastic games, but can disagree when $n>2$, via an explicit three-player counterexample. We prove existence and uniqueness of Coco-S fixed points for all two-player games and for three-player two-state games via topological degree theory, and provide an axiomatic characterization of Coco-S through a new \emph{Markov Consistency} axiom that distinguishes it from HS-S. Finally, we give sampling-based estimators with finite-sample guarantees and empirically compare the induced values, policies, and side payments on multi-player grid-game benchmarks. |
| title | Learning Strategic Value and Cooperation in Multi-Player Stochastic Games through Side Payments |
| topic | Computer Science and Game Theory Artificial Intelligence |
| url | https://arxiv.org/abs/2303.05307 |