Social Welfare Improvement for Noncooperative Dynamical Systems with Tax/Subsidy Approach

A zero-sum tax/subsidy approach is proposed to improve the social welfare. In the proposed approach, system designer modifies agents' payoff functions by collecting taxes from some agents and giving the same amount in total as subsidy to a neighbor corresponding agent(s) in the undirected tax/subsidy adjustment graph. Sufficient conditions under which agents' state converges towards the socially maximum state are derived for our proposed approach without using the information of agents' sensitivity parameters. Furthermore, a continuously Kaldor-Hicks improving tax/subsidy approach is introduced for monotonically improving agents' personal payoff over time. We present a numerical example to illustrate the efficacy of our results.