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

Angelo Fanelli (1, 2) , Michele Flammini (3, 4) , Luca Moscardelli (5)

1 CREM - Centre de recherche en économie et management
2 C2I - Centre for Computational Intelligence [Nanyang]
3 GSSI - Gran Sasso Science Institute
4 DISIM - Department of Information Engineering, Computer Science and Mathematics = Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila]
5 Dipartimento di Scienze - Universita di Chieti-Pescara

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.

Domaines: Economies et finances; Informatique [cs]

Angelo Fanelli, Michele Flammini, Luca Moscardelli. The speed of convergence in congestion games under best-response dynamics. ACM Transactions on Algorithms, 2012, 8 (3), pp.1-15. ⟨10.1145/2229163.2229169⟩. ⟨halshs-02094392⟩