Abstract
We study the problem of computing the tightest \(α\)-potential approximation of a general-sum game over continuous action spaces, within a prescribed class of potential functions and when each player has access only to its own utility function. The difficulty is twofold: the approximation error involves a worst-case search over an infinite set of unilateral deviations, and the required utility information is distributed across players. For a linear-in-parameters potential class, we use an exact finite-tuple reformulation that separates the problem into a global outer search over deviation tuples and distributed convex inner problems. We develop a primal--dual inner oracle tailored to this structure and establish a uniform one-sided accuracy guarantee. This oracle can be combined with global outer search to obtain an end-to-end guarantee on the outer optimization error. We also develop a projected zeroth-order outer method as a computationally lighter alternative for higher-dimensional problems. Numerical experiments illustrate the accuracy--computation tradeoff between the two outer-search methods and show that the proposed optimization framework can improve upon analytical \(α\)-potential constructions.
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Publication details
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Cite this article
APA 7
Chen, Y., & Maheshwari, C. (2026). Distributed Algorithms for $α$-Potential Functions in General-Sum Games. https://omanscience.com/en/articles/distributed-algorithms-for-potential-functions-in-general-sum-games
MLA 9
Chen, Yifei, and Chinmay Maheshwari. "Distributed Algorithms for $α$-Potential Functions in General-Sum Games." https://omanscience.com/en/articles/distributed-algorithms-for-potential-functions-in-general-sum-games.
Chicago (author–date)
Chen, Yifei, and Chinmay Maheshwari. 2026. "Distributed Algorithms for $α$-Potential Functions in General-Sum Games." https://omanscience.com/en/articles/distributed-algorithms-for-potential-functions-in-general-sum-games.
Harvard
Chen, Y. and Maheshwari, C. (2026) 'Distributed Algorithms for $α$-Potential Functions in General-Sum Games', Available at: https://omanscience.com/en/articles/distributed-algorithms-for-potential-functions-in-general-sum-games.
Vancouver
Chen Y, Maheshwari C. Distributed Algorithms for $α$-Potential Functions in General-Sum Games. https://omanscience.com/en/articles/distributed-algorithms-for-potential-functions-in-general-sum-games
IEEE
Y. Chen, and C. Maheshwari, "Distributed Algorithms for $α$-Potential Functions in General-Sum Games," https://omanscience.com/en/articles/distributed-algorithms-for-potential-functions-in-general-sum-games.