Computing Optimal Equilibria in Repeated Games with Restarts

Abstract

The maximum satisfiability problem (MaxSAT) is a crucial combinatorial optimization problem with widespread applications across various critical domains. This paper presents CASHWMaxSAT, an efficient core-guided MaxSAT solver based on two novel ideas. The first and most important idea is the introduction of an extended stratification technique that progressively focuses on solving high-weight soft clauses. Second, we integrate disjoint unsatisfiable cores with the goal of minimizing the unsatisfiable core, allowing the solver to learn multiple high-quality clauses in a single conflict analysis step. These innovations enable our MaxSAT solver to efficiently identify key constraints and reduce redundant reasoning, significantly enhancing solving efficiency. Experimental results on benchmarks from the complete weighted track of the MaxSAT Evaluations 2022-2024 demonstrate that the proposed methods lead to substantial improvements, with CASHWMaxSAT outperforming state-of-the-art MaxSAT solvers across all benchmarks. Additionally, it enabled us to achieve the top two positions in the exact weighted category of the MaxSAT Evaluation 2024.