Solving Imperfect-Information Dynamic Defender-Attacker Blotto Games Based on Progressive-Expanding CFR

This work studies imperfect-information dynamic Defender-Attacker Blotto games under graph constraints. In this game, two players make multi-stage decisions on how to allocate and move limited resources to control critical nodes, with each player observing only part of the opponent's resources at each stage, highlighting the challenges of imperfect information. Existing reinforcement learning methods suffer from low sample efficiency and lack theoretical guarantees, while classic counterfactual regret minimization (CFR) algorithms struggle with low computational efficiency in large action spaces. To address this, we propose a Progressive-Expanding Counterfactual Regret Minimization (PE-CFR) algorithm. This method uses hybrid strategy pruning to construct a highquality initial action subset and applies progressive expansion mechanism to explore the full action space. Experiments on networks with 3 to 6 nodes show that PE-CFR significantly outperforms the baseline in both convergence speed and computational efficiency. The equilibrium generated reveals that resource allocation strategy should consider network topology and the opponent's mobility, rather than solely consider values of nodes.