Equilibration Analysis and Control of Coordinating Decision-Making Populations

Whether a population of decision-makers reach a state of satisfactory decisions is a fundamental problem in studying collective behaviors. In the framework of evolutionary game theory, researchers used potential functions to establish equilibration under best-response and imitation update rules by imposing conditions on the individuals' utility functions, and in turn to control the population toward a desired equilibrium. Nevertheless, finding a potential function is often daunting, if not near impossible. We introduce the so-called
coordinating agent
whose tendency to switch to a decision changes only if another agent switches to that decision. We prove that any population of coordinating agents, a
coordinating population
, almost surely equilibrates. Apparently, some binary network games that were proven to equilibrate using potential functions are coordinating, and some coloring problems can be solved using this notion. We additionally show that any mixed network of agents following best-response, imitation, or rational imitation, and associated with coordination payoff matrices is coordinating, and hence, equilibrates. As a second contribution, we provide an incentive-based control algorithm that leads coordinating populations to a desired equilibrium by iteratively maximizing the ratio of the number of agents choosing the desired decision to the provided incentive. It performs near optimal and as well as specialized algorithms proposed for best-response and imitation; however, it does not require a potential function.