Optimal transport and incentive design in multi-agent economic control

This paper develops a principled framework for incentive design in multi-agent economic systems using tools from optimal transport (OT) theory and decentralized control. We consider a class of stochastic multi-agent environments in which each agent selects actions to minimize individual cost functions that depend on both private preferences and aggregate outcomes. To promote socially desirable allocations, we introduce an OT-based mechanism design approach, where incentives are computed as gradients of a Lagrangian dual formulation over probability measures. Our main results establish: (i) a KKT-type characterization of incentive compatibility in Wasserstein space, (ii) monotonicity and fairness of equilibrium allocations under convex coupling, (iii) structural convexity of cost functionals over coupled agent dynamics, (iv) convergence of iterative market updates to optimal allocations, and (v) efficiency guarantees under decentralized feedback. We demonstrate that fairness and incentive alignment emerge naturally as solutions to constrained OT problems, allowing for scalable, interpretable, and robust economic control policies. This formulation provides a unifying perspective on decentralized optimization, mechanism design, and ergodic fairness in economic networks, and opens new directions for data-driven social planning under uncertainty.