Improving approximate pure Nash equilibria in congestion games

Alexander Skopalik, Vipin Ravindran Vijayalakshmi

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Abstract

Congestion games constitute an important class of games to model resource allocation by different users. As computing an exact or even an approximate pure Nash equilibrium is in general PLS-complete, Caragiannis et al. (2011) present a polynomial-time algorithm that computes a ($2 + \epsilon$)-approximate pure Nash equilibria for games with linear cost functions and further results for polynomial cost functions. We show that this factor can be improved to $(1.61+\epsilon)$ and further improved results for polynomial cost functions, by a seemingly simple modification to their algorithm by allowing for the cost functions used during the best response dynamics be different from the overall objective function. Interestingly, our modification to the algorithm also extends to efficiently computing improved approximate pure Nash equilibria in games with arbitrary non-decreasing resource cost functions. Additionally, our analysis exhibits an interesting method to optimally compute universal load dependent taxes and using linear programming duality prove tight bounds on PoA under universal taxation, e.g, 2.012 for linear congestion games and further results for polynomial cost functions. Although our approach yield weaker results than that in Bil\`{o} and Vinci (2016), we remark that our cost functions are locally computable and in contrast to Bil\`{o} and Vinci (2016) are independent of the actual instance of the game.
Original languageEnglish
PublisherArXiv.org
DOIs
Publication statusPublished - 30 Jul 2020

Keywords

  • cs.GT

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  • Improving Approximate Pure Nash Equilibria in Congestion Games

    Ravindran Vijayalakshmi, V. & Skopalik, A., 6 Dec 2020, Web and Internet Economics: 16th International Conference, WINE 2020, Proceedings. Chen, X., Gravin, N., Hoefer, M. & Mehta, R. (eds.). Springer, p. 280-294 15 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 12495 LNCS).

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