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arXiv · 2512.05667

On Dynamic Programming Theory for Leader-Follower Stochastic Games

Jilles Steeve Dibangoye·Thibaut Le Marre·Ocan Sankur·François Schwarzentruber
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Abstract

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 {\epsilon}-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.

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Jilles Steeve Dibangoye, Thibaut Le Marre, Ocan Sankur, François Schwarzentruber. 2025-12-05. On Dynamic Programming Theory for Leader-Follower Stochastic Games. https://arxiv.org/abs/2512.05667

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