Control of Learning in Anticoordination Network Games

Many games have undesirable Nash equilibria. In such games, a designer's goal is to avoid “bad” equilibria. In this article, we focus on which players to control and how to control them so that the emerging outcome of learning dynamics is desirable. In particular, we consider best-response-type learning dynamics for an anticoordination network game. The designer's goal is to achieve maximum anticoordination with the fewest number of players to control at each round. Our analysis shows that despite the incentive to anticoordinate with neighbors, selfish agents may fail to do so. Accordingly, we relate optimal policies for obtaining maximum anticoordination to the set of Nash equilibria. Noting the combinatorial problem of optimally selecting players in benchmark networks, we develop suboptimal solutions via solving a minimum vertex-cover problem, and by greedily selecting players based on their potential to induce cascading effects. Numerical experiments on random networks show that the cascade-based greedy algorithm can lower the control effort significantly compared to random public advertising policies. Moreover, its control effort is no more than twice the optimal control effort in the worst case.