🤖 AI Summary
This work addresses the challenge of incentive design under information asymmetry, where a system planner cannot observe agents’ sensitivity to incentives, rendering conventional hypergradient-based methods ineffective. The authors propose a “social gradient flow” mechanism that leverages the gradient of social cost with respect to joint actions to guide incentive adjustments, thereby aligning self-interested agent behavior with system-wide optimality without requiring knowledge of individual cost structures. Theoretically, this gradient is shown to always constitute a descent direction for the planner’s objective. A two-timescale dynamical framework is developed to ensure convergence even when equilibria are unobservable: under full observability, it converges to the unique socially optimal incentive; under partial observability, it still asymptotically converges in conjunction with any equilibrium-learning rule that tracks equilibria over time. Numerical experiments corroborate the efficacy of the proposed approach.
📝 Abstract
Incentive design problems consider a system planner who steers self-interested agents toward a socially optimal Nash equilibrium by issuing incentives in the presence of information asymmetry, that is, uncertainty about the agents' cost functions. A common approach formulates the problem as a Mathematical Program with Equilibrium Constraints (MPEC) and optimizes incentives using hypergradients-the total derivatives of the planner's objective with respect to incentives. However, computing or approximating the hypergradients typically requires full or partial knowledge of equilibrium sensitivities to incentives, which is generally unavailable under information asymmetry. In this paper, we propose a hypergradient-free incentive law, called the social-gradient flow, for incentive design when the planner's social cost depends on the agents' joint actions. We prove that the social cost gradient is always a descent direction for the planner's objective, irrespective of the agent cost landscape. In the idealized setting where equilibrium responses are observable, the social-gradient flow converges to the unique socially optimal incentive. When equilibria are not directly observable, the social-gradient flow emerges as the slow-timescale limit of a two-timescale interaction, in which agents' strategies evolve on a faster timescale. It is established that the joint strategy-incentive dynamics converge to the social optimum for any agent learning rule that asymptotically tracks the equilibrium. Theoretical results are also validated via numerical experiments.