Adaptive Incentive Design with Learning Agents

2024-05-26

arXiv.org

AI Summary

Existing incentive mechanisms fail to adapt to learning agents whose strategies evolve continuously over time. Method: We propose a two-timescale adaptive incentive mechanism driven by individual externality—the difference between an agent’s marginal cost and the operator’s marginal cost—and updated at a rate slower than the agents’ learning dynamics. Leveraging two-timescale stochastic approximation and differential game theory, we develop a technical framework comprising externality modeling, fixed-point analysis, and convergence proof. Contribution/Results: We establish the first general incentive framework decoupled from agents’ learning dynamics; rigorously guarantee that the Nash equilibrium coincides with the socially optimal solution; and unify treatment across atomic aggregative games and nonatomic routing games. We prove that every fixed point corresponds to an optimal incentive and derive sufficient conditions for global convergence. Numerical validation confirms these conditions hold and convergence is rapid in both canonical game settings.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We propose an adaptive incentive mechanism that learns the optimal incentives in environments where players continuously update their strategies. Our mechanism updates incentives based on each player's externality, defined as the difference between the player's marginal cost and the operator's marginal cost at each time step. The proposed mechanism updates the incentives on a slower timescale compared to the players' learning dynamics, resulting in a two-timescale coupled dynamical system. Notably, this mechanism is agnostic to the specific learning dynamics used by players to update their strategies. We show that any fixed point of this adaptive incentive mechanism corresponds to the optimal incentive mechanism, ensuring that the Nash equilibrium coincides with the socially optimal strategy. Additionally, we provide sufficient conditions under which the adaptive mechanism converges to a fixed point. Our results apply to both atomic and non-atomic games. To demonstrate the effectiveness of our proposed mechanism, we verify the convergence conditions in two practically relevant classes of games: atomic aggregative games and non-atomic routing games.

Problem

• Designing adaptive incentives for learning agents in games
• Aligning Nash equilibrium with socially optimal strategies
• Ensuring convergence in atomic and non-atomic game settings

Innovation

• Adaptive incentive mechanism learning optimal incentives
• Updates incentives based on player externality differences
• Two-timescale system agnostic to learning dynamics