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TL;DR#
Congestion games model scenarios where self-interested players share resources, leading to suboptimal outcomes. Existing tax design methods often assume complete knowledge of the game, a limitation in many real-world settings. This significantly hinders the design of effective tax policies that ensure optimal resource utilization. The problem is exacerbated by the exponentially large space of possible tax functions.
This paper tackles this challenge by proposing a new learning-based algorithm that finds near-optimal tax designs using only equilibrium feedback from the game. This method employs several innovative techniques, including piecewise linear approximation of the tax function, adding extra terms to guarantee strong convexity, and the design of an efficient subroutine to find exploratory taxes. The algorithm achieves a sample complexity that scales polynomially with the number of facilities and the smoothness of the cost function, proving its efficiency and practicality for real-world applications. The findings pave the way for more sophisticated and data-driven approaches to optimal tax design in various real-world settings.
Key Takeaways#
Why does it matter?#
This paper is important because it presents the first algorithm for learning optimal tax design in congestion games with limited feedback. This is a significant contribution to the field of algorithmic game theory, as it addresses a long-standing challenge of designing efficient mechanisms to induce socially optimal behavior in complex systems where players act selfishly. The algorithm is computationally efficient and has provable guarantees on its performance, making it suitable for real-world applications. The work also opens up new avenues of research by introducing the concept of ’equilibrium feedback’ and proposing novel techniques for function approximation and exploratory tax design. These contributions will likely inspire further research on learning-based approaches to mechanism design in various contexts.
Visual Insights#
This figure shows the performance of the proposed algorithm for learning optimal tax design in congestion games, in terms of social welfare. The algorithm is tested under different parameters (c and p), which represent the cost function parameters in the game. The plots illustrate that the algorithm quickly converges to the optimal social welfare value across different parameter settings, demonstrating its effectiveness in finding near-optimal tax strategies.
This protocol describes the online tax design process for congestion games. It iteratively involves the designer choosing a tax, observing the resulting Nash equilibrium load and cost, and using this feedback to inform subsequent tax choices. The goal is to learn an optimal tax that minimizes social cost.
Full paper#
