Verifying Equilibria in Finite-Horizon Probabilistic Concurrent Game Systems
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| Format: | Preprint |
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2025
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| author | Rajasekaran, Senthil Vardi, Moshe Y. |
| author_facet | Rajasekaran, Senthil Vardi, Moshe Y. |
| contents | Finite-horizon probabilistic multiagent concurrent game systems, also known as finite multiplayer stochastic games, are a well-studied model in computer science due to their ability to represent a wide range of real-world scenarios involving strategic interactions among agents over a finite amount of iterations (given by the finite-horizon). The analysis of these games typically focuses on evaluating (verifying) and computing (synthesizing/realizing) which strategy profiles (functions that represent the behavior of each agent) qualify as equilibria. The two most prominent equilibrium concepts are the Nash equilibrium and the subgame perfect equilibrium, with the latter considered a conceptual refinement of the former. Computing these equilibria from scratch is, however, often computationally infeasible. Therefore, recent attention has shifted to the verification problem, where a given strategy profile must be evaluated to determine whether it satisfies equilibrium conditions. In this paper, we demonstrate that the verification problem for subgame perfect equilibria lies in PSPACE, while for Nash equilibria, it is EXPTIME-complete. This is a highly counterintuitive result since subgame perfect equilibria are often seen as a strict strengthening of Nash equilibria and are intuitively seen as more complicated. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_14690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Verifying Equilibria in Finite-Horizon Probabilistic Concurrent Game Systems Rajasekaran, Senthil Vardi, Moshe Y. Computer Science and Game Theory Logic in Computer Science Finite-horizon probabilistic multiagent concurrent game systems, also known as finite multiplayer stochastic games, are a well-studied model in computer science due to their ability to represent a wide range of real-world scenarios involving strategic interactions among agents over a finite amount of iterations (given by the finite-horizon). The analysis of these games typically focuses on evaluating (verifying) and computing (synthesizing/realizing) which strategy profiles (functions that represent the behavior of each agent) qualify as equilibria. The two most prominent equilibrium concepts are the Nash equilibrium and the subgame perfect equilibrium, with the latter considered a conceptual refinement of the former. Computing these equilibria from scratch is, however, often computationally infeasible. Therefore, recent attention has shifted to the verification problem, where a given strategy profile must be evaluated to determine whether it satisfies equilibrium conditions. In this paper, we demonstrate that the verification problem for subgame perfect equilibria lies in PSPACE, while for Nash equilibria, it is EXPTIME-complete. This is a highly counterintuitive result since subgame perfect equilibria are often seen as a strict strengthening of Nash equilibria and are intuitively seen as more complicated. |
| title | Verifying Equilibria in Finite-Horizon Probabilistic Concurrent Game Systems |
| topic | Computer Science and Game Theory Logic in Computer Science |
| url | https://arxiv.org/abs/2503.14690 |