Incentive Mechanisms for Welfare Maximization Under Individual Rationality in Noncooperative Dynamical Systems

Abstract

Human societies are shaped by strategic interactions among self-interested decision-makers, where conflicts between individual and social interests naturally arise. This paper investigates the design of incentive mechanism for multi-agent game systems to reconcile social welfare maximization with individual benefits under economic constraints. We develop a linear-quadratic incentive framework to reshape Nash equilibria while reconciling the constraints of Pareto efficiency, individual rationality, and budget balance. The optimal target state is identified as the solution of a constrained optimization problem associated with the social welfare and aggregated payoff functions. Our theoretical analysis characterizes the conditions of incentive functions that steer self-interested agents towards the optimal target state as a Pareto-efficient Nash equilibrium for achieving the maximum attainable social welfare. We further characterize how the choice of social welfare function constrains achievable individual outcomes, revealing a structural paradox associated with priority weighting under individual rationality. Several numerical examples are presented to demonstrate the efficacy of our results.