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. 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 {mathcal {O}}(m{n}) to {mathcal {O}}(mn) and thereby mitigates computational complexity. 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 problem involving four thousand times more joint actions while yielding similar or better performance in terms of a fairness indicator and showing a maximum optimality gap of 0.066% in terms of the average delay cost. In the meantime, it yields a solution that shows up to 99.5% improvement in a fairness indicator and up to 50.4% reduction in average delay cost compared to the Nash solution, which does not involve coordination.