A Library for Algorithmic Game Theory in Ssreflect/Coq

Alexander Bagnall, Samuel Merten, Gordon Stewart

Abstract


We report on the formalization in Ssreflect/Coq of a number of concepts and results from algorithmic game theory, including potential games, smooth games, solution concepts such as Pure and Mixed Nash Equilibria, Coarse Correlated Equilibria, epsilon-approximate equilibria, and behavioral models of games such as best-response dynamics. We apply the formalization to prove  Price of Stability bounds for, and convergence under best-response dynamics of, the Atomic Routing game, which has applications in computer networking. Our second application proves that Affine Congestion games are (5/3, 1/3)-smooth, and therefore have Price of Anarchy 5/2. Our formalization is available online.

Keywords


Coq; Ssreflect; Algorithmic Game Theory

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DOI: 10.6092/issn.1972-5787/7235

Copyright (c) 2017 Alexander Bagnall, Samuel Merten, Gordon Stewart

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This work is licensed under a Creative Commons Attribution 3.0 Unported License.