Towards Optimal Control of Evolutionary Games on Networks

We investigate the control of evolutionary games on networks, in which each edge represents a two-player repeating game between neighboring agents. After each round of games, agents can imitate the strategies of better performing neighbors, while a subset of agents can be assigned strategies and thus serve as control inputs. We seek here the smallest set of control agents needed to drive the network to a desired uniform strategy state. After presenting exact solutions for complete and star networks and describing a general solution approach that is computationally practical only for small networks, we design a fast algorithm for approximating the solution on arbitrary networks using a weighted minimum spanning tree and strategy propagation algorithm. The resulting approximation is exact for certain classes of games on complete and star networks and simulations suggest that the algorithm performs well in more general cases.