Pareto-Improving Incentive Mechanism for Noncooperative Dynamical Systems Under Sustainable Budget Constraint

A Pareto-improving incentive mechanism to improve the weighted social welfare and achieve continual Pareto improvement for a pseudogradient-based noncooperative dynamical system is developed. In the proposed approach, the system manager remodels agents' dynamical decision-making by collecting taxes from some agents and giving some of the collected taxes to other agents as subsidies with a sustainable budget constraint. Sufficient conditions are derived under which agents' state converges toward the socially maximum state associated with a weighted social welfare function depending on the priority ratio of the agents and the initial state. We present several illustrative numerical examples to illustrate the efficacy of our results and reveal the fact that the potentialization of the payoff structure has a very strong relation to generating Pareto-improving system trajectories.