The speed of convergence in congestion games under best-response dynamics

Authors:
Angelo Fanelli;Michele Flammini;Luca Moscardelli
Affiliations:
Nanyang Technological University, Singapore;University of L'Aquila, Italy;University of Chieti-Pescara, Italy
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2012

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Abstract

We investigate the speed of convergence of best response dynamics to approximately optimal solutions in congestion games with linear delay functions. In Ackermann et al. [2008] it has been shown that the convergence time of such dynamics to Nash equilibrium may be exponential in the number of players n. Motivated by such a negative result, we focus on the study of the states (not necessarily being equilibria) reached after a limited number of players' selfish moves, and we show that Θ(n log log n) best responses are necessary and sufficient to achieve states that approximate the optimal solution by a constant factor, under the assumption that every O(n) steps each player performs a constant (and nonnull) number of best responses. We show that such result is tight also for the simplest case of singleton congestion games.