Social Welfare Maximization in Noncooperative Dynamical Systems With Privacy-Preserving Incentive Mechanism

A privacy-preserving incentive mechanism to maximize the weighted social welfare for pseudo-gradient-based noncooperative dynamical systems is developed. Sensitive information that could reveal the payoff functions is referred to as the privacy of agents. In the proposed approach, at least half of the agents (named as nonessential agents) can provide some nonsensitive information in addition to their state values, enabling the system manager to influence agents' dynamical decisions by imposing taxes or offering subsidies with a sustainable budget constraint. To protect the privacy of all agents, our approach shifts the stationary points of the nonessential agents and hence indirectly moves the Nash equilibrium of the entire system. By constructing the additional nonsensitive information from nonessential agents as the time-wise information of stationary-point mappings related to certain secret matrices, sufficient conditions are derived where the Nash equilibrium is shifted towards the target state achieving Pareto efficiency under the incentive mechanism. We also provide some stability conditions to ensure that agents' state converges to the target state under a sustainable budget for the given initial state. Several numerical examples are used to illustrate the efficacy of our results.