Nash Equilibrium Computation

The field studies how to find strategy profiles in which no player can improve by changing strategy alone, across settings such as matrix games, Markov games, auctions, and poker. Methods include regret minimization and counterfactual regret minimization, best-response and fictitious-play dynamics, mirror-descent methods, and optimization formulations such as linear complementarity problems and quadratic programs. Researchers also use reinforcement learning and offline data to estimate equilibria when payoffs or transitions are unknown, with exploitability, regret, and equilibrium residuals serving as common evaluation measures. A central tension is that scalable methods often provide approximate or average-iterate guarantees, while exact computation, last-iterate convergence, and principled equilibrium selection remain difficult in multiplayer and imperfect-information games.