  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 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.
