Convergence analysis and control of evolutionary matrix-game dynamics

Networks of decision-making individuals with simple dynamics may give rise to complex and seemingly unpredictable collective behaviors which may have negative consequences such as traffic jams and market crashes or positive outcomes such as volunteer disaster relief and free-market stabilization. Usually on one hand, there is a group task requiring the individuals to cooperate to optimize the collective performances, and on the other, each individual is self-interested and may prefer to prioritize her own interest over the group task, resulting in a social dilemma. Typical research questions in this topic therefore focus on (i) how to predict the long run behavior of the networks and find factors causing non-converging fluctuations in the actions of the individuals; (ii) how to build a model to describe the dynamics as cooperation evolves or is promoted among selfish individuals; and (iii) how to control the number of individuals taking a particular action in a network. We tackle these problems by modeling networks of decision-making individuals using evolutionary matrix-game dynamics, performing convergence analysis to understand the asymptotic behavior of the dynamics, and designing control algorithms to lead the individuals to a desired action.