Controlling Networks of Imitative Agents

We consider how asynchronous networks of agents who imitate their highest-earning neighbors can be efficiently driven towards a desired strategy by offering payoff incentives, either uniformly or targeted to individuals. In particular, if for each available strategy, agents playing that strategy receive maximum payoff when their neighbors play that same strategy, we show that providing incentives to agents in a network that is at equilibrium will result in convergence to a unique equilibrium. When a uniform incentive can be offered to all agents, one can compute the optimal incentive using a binary search algorithm. When incentives can be targeted to individuals, we propose an algorithm to select which agents should be chosen based on iteratively maximizing a ratio of the number of agents who adopt the desired strategy to the payoff incentive required to get those agents to do so. Simulations demonstrate that this algorithm computes near-optimal targeted payoff incentives for a range of networks and payoff distributions in coordination games