Title: Control of Asynchronous Imitation Dynamics on Networks,
Abstract: Imitation is widely observed in populations of decision-making agents. Using
our recent convergence results for asynchronous imitation dynamics on networks,
we consider how such networks can be efficiently driven to a desired
equilibrium state by offering payoff incentives for using a certain strategy,
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 new equilibrium. For the case when a uniform incentive can be offered to
all agents, this result allows the computation of the optimal incentive using a
binary search algorithm. When incentives can be targeted to individual agents,
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 the proposed algorithm computes near-optimal
targeted payoff incentives for a range of networks and payoff distributions in
coordination games.