Quantum-Assisted Computation for Nash Equilibrium in Bimatrix Games

Nash equilibrium (NE) computation is a fundamental problem in game theory, with numerous applications in economics, control theory, computer science, and engineering. However, finding an NE remains computationally challenging, even in two-player normal-form games. In this work, we leverage quantum computing (QC) to develop an efficient quantum annealing-based algorithm for computing NEs in two-player non-cooperative games. Our approach exploits quantum parallelism to enhance computational efficiency. We first formulate the NE computation as a non-convex quadratic problem, which is then transformed into a quadratic unconstrained binary optimization (QUBO) problem through the use of penalization techniques. This reformulation is amenable to quantum annealing solvers. However, due to the probabilistic nature of quantum annealing, the solver typically returns a distribution of candidate solutions, which may not directly correspond to valid NEs. To address this, we propose a novel QA-assisted algorithm that incorporates a post-quantum processing step to refine, verify, and select approximate NEs from the sampled solutions. The effectiveness of the proposed algorithm is demonstrated through experimental validation, highlighting the potential of QC in solving complex equilibrium computation problems.