Control of Asynchronous Imitation Dynamics on Networks

TL;DR

This paper studies how to efficiently steer networks of decision-making agents towards a desired equilibrium by offering strategic incentives, using convergence results for asynchronous imitation dynamics and algorithms for optimal incentive design.

Contribution

It introduces methods for computing optimal uniform and targeted incentives to control imitation dynamics on networks, supported by convergence analysis and simulation results.

Findings

Incentives lead to convergence to a unique equilibrium.

Binary search algorithm effectively computes optimal uniform incentives.

Iterative algorithm selects targeted agents to maximize incentive efficiency.

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.