A Library for Algorithmic Game Theory in Ssreflect/Coq
Keywords:Coq, Ssreflect, Algorithmic Game Theory
AbstractWe 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.
How to Cite
Bagnall, A., Merten, S., & Stewart, G. (2017). A Library for Algorithmic Game Theory in Ssreflect/Coq. Journal of Formalized Reasoning, 10(1), 67–95. https://doi.org/10.6092/issn.1972-5787/7235
Copyright (c) 2017 Alexander Bagnall, Samuel Merten, Gordon Stewart
Copyrights and publishing rights of all the texts on this journal belong to the respective authors without restrictions.