Towards control of evolutionary games on networks

We investigate a problem related to the control of evolutionary games on networks, in which the nodes represent agents engaged in multiple simultaneous 2-player evolutionary games and the edges define who plays with whom. The strategy dynamics are governed by a deterministic evolutionary update rule, while a set of control agents can be fixed to a desired strategy for the duration of the game. We seek here the smallest set of control agents which will result in all agents in the network converging to the desired strategy. We address network types in order of increasing complexity, first providing analytical solutions or bounds for an evolutionary prisoner´s dilemma game on reglar networks and trees, and then presenting an algorithm that uses graph partitioning to recursively decompose a larger problem into several smaller problems, the solutions to which can be used to construct an approximate solution on the original network at greatly reduced computation. Finally, we provide simulations to demonstrate that this algorithm finds a near-optimal control set in the majority of cases.