Improving Approximate Pure Nash Equilibria in Congestion Games

Abstract

Congestion games constitute an important class of games to model resource allocation by different users. As computing an exact [18] or even an approximate [34] pure Nash equilibrium is in general PLScomplete, Caragiannis et al. [9] present a polynomial-time algorithm that computes a (2 + )-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 + ) 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 the 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 Bilò and Vinci [6], we remark that our cost functions are locally computable and in contrast to [6] are independent of the actual instance of the game. Keywords: Congestion games • Approximate pure Nash equilibria • Price of anarchy • Universal taxes V. R. Vijayalakshmi-This work is supported by the German research council (DFG) Research Training Group 2236 UnRAVeL

The Impact of Selfish Behavior in Load Balancing Games

“…For the special case of load balancing games on identical resources, the works of [45] and [20] show that the price of anarchy is 2.012067 for unweighted games and at least 5/2 for weighted ones. The works of [42,46] generalize the above results on affine unweighted games with identical resources, and provide tight bounds on the price of anarchy even for polynomial and more general latencies. In [40], it is proved that, for symmetric load balancing games, the price of anarchy drops to 4/3 if the games are unweighted, and to 9/8 if the games are weighted with identical resources.…”

“…Previous work established that the price of anarchy does not improve when restricting to unweighted load balancing games with polynomial latency functions [20,32], while better bounds are possible in unweighted symmetric load balancing games with fairly general latency functions [28]. Under the assumption of identical resources, improvements are also possible in the following cases: unweighted load balancing games with affine latencies [20,45], unweighted games with polynomial or general latencies [42,46], weighted symmetric load balancing games with affine latencies [40] or monomial latencies [30]. Finally, [7] proves that the price of anarchy does not improve when restricting to weighted symmetric load balancing games under polynomial latency functions.…”

Enhancing the Efficiency of Altruism and Taxes in Affine Congestion Games through Signalling

“…A fundamental question in this domain is whether better performances can be obtained when applying plausible changes to the game model. Among these, we consider two well-studied scenarios: partially altruistic players (Bilò 2014;Hoefer and Skopalik 2013) and resource taxation (Bilò and Vinci 2019;Paccagnan and Gairing 2021;Vijayalakshmi and Skopalik 2020).…”