Coordination in Noncooperative Multiplayer Matrix Games via Reduced Rank Correlated Equilibria

Coordination in multiplayer games enables players to avoid the lose-lose outcome that often arises at Nash equilibria. However, designing a coordination mechanism typically requires the consideration of the joint actions of all players, which becomes intractable in large-scale games. We develop a novel coordination mechanism, termed reduced rank correlated equilibria, which reduces the number of joint actions to be considered and thereby mitigates computational complexity. The idea is to approximate the set of all joint actions with the actions used in a set of pre-computed Nash equilibria via a convex hull operation. In a game with n players and each player having m actions, the proposed mechanism reduces the number of joint actions considered from O(m^n) to O(mn). We demonstrate the application of the proposed mechanism to an air traffic queue management problem. Compared with the correlated equilibrium-a popular benchmark coordination mechanism-the proposed approach is capable of solving a queue management problem involving four thousand times more joint actions. In the meantime, it yields a solution that shows a 58.5% to 99.5% improvement in the fairness indicator and a 1.8% to 50.4% reduction in average delay cost compared to the Nash solution, which does not involve coordination.