On Dynamic Programming Theory for Leader-Follower Stochastic Games
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arXiv
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| Format: | Preprint |
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2025
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| author | Dibangoye, Jilles Steeve Marre, Thibaut Le Sankur, Ocan Schwarzentruber, François |
| author_facet | Dibangoye, Jilles Steeve Marre, Thibaut Le Sankur, Ocan Schwarzentruber, François |
| contents | Leader-follower general-sum stochastic games (LF-GSSGs) model sequential decision-making under asymmetric commitment, where a leader commits to a policy and a follower best responds, yielding a strong Stackelberg equilibrium (SSE) with leader-favourable tie-breaking. This paper introduces a dynamic programming (DP) framework that applies Bellman recursion over credible sets-state abstractions formally representing all rational follower best responses under partial leader commitments-to compute SSEs. We first prove that any LF-GSSG admits a lossless reduction to a Markov decision process (MDP) over credible sets. We further establish that synthesising an optimal memoryless deterministic leader policy is NP-hard, motivating the development of ε-optimal DP algorithms with provable guarantees on leader exploitability. Experiments on standard mixed-motive benchmarks-including security games, resource allocation, and adversarial planning-demonstrate empirical gains in leader value and runtime scalability over state-of-the-art methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Dynamic Programming Theory for Leader-Follower Stochastic Games Dibangoye, Jilles Steeve Marre, Thibaut Le Sankur, Ocan Schwarzentruber, François Computer Science and Game Theory Artificial Intelligence F.2.2; I.2.8; I.2.11; G.3 Leader-follower general-sum stochastic games (LF-GSSGs) model sequential decision-making under asymmetric commitment, where a leader commits to a policy and a follower best responds, yielding a strong Stackelberg equilibrium (SSE) with leader-favourable tie-breaking. This paper introduces a dynamic programming (DP) framework that applies Bellman recursion over credible sets-state abstractions formally representing all rational follower best responses under partial leader commitments-to compute SSEs. We first prove that any LF-GSSG admits a lossless reduction to a Markov decision process (MDP) over credible sets. We further establish that synthesising an optimal memoryless deterministic leader policy is NP-hard, motivating the development of ε-optimal DP algorithms with provable guarantees on leader exploitability. Experiments on standard mixed-motive benchmarks-including security games, resource allocation, and adversarial planning-demonstrate empirical gains in leader value and runtime scalability over state-of-the-art methods. |
| title | On Dynamic Programming Theory for Leader-Follower Stochastic Games |
| topic | Computer Science and Game Theory Artificial Intelligence F.2.2; I.2.8; I.2.11; G.3 |
| url | https://arxiv.org/abs/2512.05667 |