Reconciling Selfish Routing with Social Good
- 812 Downloads
Selfish routing is a central problem in algorithmic game theory, with one of the principal applications being that of routing in road networks. Inspired by the emergence of routing technologies and autonomous driving, we revisit selfish routing and consider three possible outcomes of it: (i) \(\theta \)-Positive Nash Equilibrium flow, where every path that has non-zero flow on all of its edges has cost no greater than \(\theta \) times the cost of any other path, (ii) \(\theta \)-Used Nash Equilibrium flow, where every used path that appears in the path flow decomposition has cost no greater than \(\theta \) times the cost of any other path, and (iii) \(\theta \)-Envy Free flow, where every path that appears in the path flow decomposition has cost no greater than \(\theta \) times the cost of any other path in the path flow decomposition. We first examine the relations of these outcomes among each other and then measure their possible impact on the network’s performance. Right after, we examine the computational complexity of finding such flows of minimum social cost and give a range for \(\theta \) for which this task is easy and a range of \(\theta \) for which this task is NP-hard for the concepts of \(\theta \)-Used Nash Equilibrium flow and \(\theta \)-Envy Free flow. Finally, we propose strategies which, in a worst-case approach, can be used by a central planner in order to provide good \(\theta \)-flows.
KeywordsSelﬁsh Routing Minimum Social Cost Nash Equilibrium (NE) Polynomial Latency Functions Atomic Congestion Games
This work was supported in part by NSF grant numbers CCF-1216103, CCF-1350823 and CCF-1331863. Part of the research was performed while a subset of the authors were at the Simons Institute in Berkeley, CA in Fall 2015.
- 1.Basu, S., Yang, G., Lianeas, T., Nikolova, E., Chen, Y.: Reconciling selfish routing with social good. arXiv:1707.00208 (2017)
- 2.Beckmann, M., McGuire, C., Winsten, C.B.: Studies in the economics of transportation. Technical report (1956)Google Scholar
- 7.Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 311–322. Springer, Heidelberg (2006). doi: 10.1007/11786986_28CrossRefzbMATHGoogle Scholar
- 8.Chien, S., Sinclair, A.: Convergence to approximate nash equilibria in congestion games. In: SODA (2007)Google Scholar
- 10.Correa, J.R., Schulz, A.S., Stier Moses, N.E.: Computational complexity, fairness, and the price of anarchy of the maximum latency problem. In: Bienstock, D., Nemhauser, G. (eds.) IPCO 2004. LNCS, vol. 3064, pp. 59–73. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-25960-2_5CrossRefzbMATHGoogle Scholar
- 15.Fleischer, L., Jain, K., Mahdian, M.: Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games. In: FOCS (2004)Google Scholar
- 16.Harks, T.: On the price of anarchy of network games with nonatomic and atomic players. Technical report, available at Optimization Online (2007)Google Scholar
- 19.Roughgarden, T.: Stackelberg scheduling strategies. In: STOC (2001)Google Scholar
- 20.Roughgarden, T.: How unfair is optimal routing? In: SODA (2002)Google Scholar
- 24.Wardrop, J.G.: Some Theoretical Aspects of Road Traffic Research (1952)Google Scholar