MM algorithm finds optimal equilibrium in coordination games faster

This paper tackles coordination games where each agent's utility combines a social component and an individual cost (or reward) that agents perceive irrationally. Such games often have multiple equilibria, making it hard to predict outcomes. The authors regularize the game by adding a strongly concave perturbation, which yields a strictly concave potential function. This regularization selects a unique equilibrium that is an epsilon-equilibrium of the original game, with epsilon controlled by the regularization strength. This approach elegantly handles irrationality and ensures a well-defined target for learning.

The core contribution is a minorization-maximization (MM) based iterative algorithm that provably converges to this potential-optimal equilibrium. MM constructs a surrogate function that minorizes the potential at each step, then maximizes it—a technique known for its monotonic convergence and numerical stability. The paper shows MM outperforms standard gradient ascent and best-response dynamics in both convergence speed and robustness, especially in high-dimensional or ill-conditioned settings. This makes the method practical for large-scale multi-agent coordination problems in economics, robotics, and AI systems where agents must align incentives without full rationality.