Learning Optimal Tax Design in Nonatomic Congestion Games

2024-02-12

arXiv.org

AI Summary

This work studies learning optimal taxation mechanisms in nonatomic congestion games using only equilibrium feedback—i.e., observations of Nash equilibrium outcomes—with the objective of maximizing social welfare. Addressing challenges including limited information, nonconvexity, nondifferentiability, and high dimensionality of tax functions, we propose the first equilibrium-feedback learning framework for taxation. We introduce piecewise-linear tax functions and strongly convex potential functions to enhance learnability. Furthermore, we design an efficient gradient-free learning algorithm that balances exploration and exploitation. Theoretically, we establish a sample complexity of $O(eta F^2 / varepsilon)$, guaranteeing $varepsilon$-accuracy convergence to the optimal tax mechanism. This is the first work to achieve taxation mechanism learning solely from equilibrium feedback, circumventing the conventional requirements of full model knowledge or gradient information.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In multiplayer games, self-interested behavior among the players can harm the social welfare. Tax mechanisms are a common method to alleviate this issue and induce socially optimal behavior. In this work, we take the initial step of learning the optimal tax that can maximize social welfare with limited feedback in congestion games. We propose a new type of feedback named emph{equilibrium feedback}, where the tax designer can only observe the Nash equilibrium after deploying a tax plan. Existing algorithms are not applicable due to the exponentially large tax function space, nonexistence of the gradient, and nonconvexity of the objective. To tackle these challenges, we design a computationally efficient algorithm that leverages several novel components: (1) a piece-wise linear tax to approximate the optimal tax; (2) extra linear terms to guarantee a strongly convex potential function; (3) an efficient subroutine to find the exploratory tax that can provide critical information about the game. The algorithm can find an $epsilon$-optimal tax with $O(eta F^2/epsilon)$ sample complexity, where $eta$ is the smoothness of the cost function and $F$ is the number of facilities.

Problem

• Multi-agent systems
• Optimal taxation
• Information constraints

Innovation

• Optimal Taxation Design
• Equilibrium Feedback
• Limited Information Strategies