Abstract
Previous works on the inefficiency of selfish routing have focused on the Wardropian traffic equilibria with an infinite number of infinitesimal players, each controlling a negligible fraction of the overall traffic, but only very limited pseudo-approximation results have been obtained for the atomic selfish routing game with a finite number of players. In this note we examine the price of anarchy of selfish routing with atomic Cournot–Nash players, each controlling a strictly positive splittable amount of flow. We obtain an upper bound of the inefficiency of equilibria with polynomial cost functions, and show that the bound is 1 or there is no efficiency loss when there is only one player, and the bound reduces to the result established in the literature when there are an infinite number of infinitesimal players.
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References
Altman E, Basar T, Jimenez T, Shimkin N (2002) Competitive routing in networks with polynomial costs. IEEE Trans Automat Contr 47:92–96
Awerbuch B, Azar Y, Epstein A (2005) The price of routing unsplittable flow. In: Proceedings of the 37th ACM Symposium on the theory of computing (to appear)
Chau CK, Sim KM (2003) The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands. Oper Res Lett 31:327–334
Correa JR, Schulz AS, Stier-Moses NE (2004) Selfish routing in capacitated networks. Math Oper Res 29:961–976
Correa JR, Schulz AS, Stier Moses NE (2005) On the inefficiency of equilibria in congestion games. In: Proceedings of the 11th Conference on Integer Programming and Combinatorial Optimization (IPCO 2005) (to appear)
Harker PT (1988) Multiple equilibrium behaviors on networks. Transp Sci 22:39–46
Haurie A, Marcotte P (1985) On the relationship between Nash–Cournot and Wardrop equilibria. Networks 15:295–308
Papadimitriou CH (2001) Algorithms, games, and the internet. In: Proceedings of the 33rd Annual ACM Symposium on the theory of computing, pp 749–753
Perakis G (2004) The price of anarchy when costs are nonlinear and asymmetric. Lect Notes Comput Sci 3064:46–58. Springer
Roughgarden T (2003) The price of anarchy is independent of the network topology. J Comput Syst Sci 67:341–364
Roughgarden T (2005a) Selfish routing and the price of anarchy. The MIT Press, Cambridge
Roughgarden T (2005b) Selfish routing with atomic players. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA05), pp 1184–1185
Roughgarden T, Tardos E (2002) How bad is selfish routing? J ACM 49:236–259
Roughgarden T, Tardos E (2004) Bounding the inefficiency of equilibria in non-atomic congestion games. Games Econom Behav 47:389–403
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Yang, H., Han, D. & Lo, H.K. Efficiency of Atomic Splittable Selfish Routing with Polynomial Cost Functions. Netw Spat Econ 8, 443–451 (2008). https://doi.org/10.1007/s11067-007-9017-8
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DOI: https://doi.org/10.1007/s11067-007-9017-8