Abstract
We focus on the problem of scheduling n weighted selfish tasks on m identical parallel machines and we study the performance of nonpreemptive coordination mechanisms. A nonpreemptive coordination mechanism consists of m local scheduling policies that decide the processing order of the tasks on each machine without delays or interruptions. We discuss the existence of Nash equilibria for this setting and show that it is not a guaranteed property of all nonpreemptive coordination mechanisms. Next, we focus on the wider class of randomized Nash equilibria and prove lower bounds on the price of anarchy. Our lower bounds are presented in comparison to the currently best known coordination mechanism (which uses delays) and lead to the conclusion that preemption or delays are required in order to improve on the currently best known solution.
Similar content being viewed by others
References
Angel, E., Bampis, E., Pascual, F.: Truthful algorithms for scheduling selfish tasks on parallel machines. Theor. Comput. Sci. 369(1–3), 157–168 (2006)
Awerbuch, B., Azar, Y., Richter, Y., Tsur, D.: Trade-offs in worst-case equilibria. In: Proc. WAOA, pp. 41–52 (2003)
Bagchi, A.: Stackelberg Differential Games in Economic Models. Lecture Notes in Control and Information Sciences, vol. 64. Springer, Berlin (1984)
Beckmann, M., McGuire, C.B., Winstein, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)
Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. In: Proc. ICALP, pp. 311–322 (2006)
Christodoulou, G., Koutsoupias, E., Nanavati, A.: Coordination mechanisms. In: Proc. ICALP, pp. 345–357 (2004)
Cole, R., Dodis, Y., Roughgarden, T.: How much can taxes help selfish routing? In: Proc. ACM EC, pp. 98–107 (2003)
Czumaj, A.: Selfish routing on the Internet. In: Handbook of Scheduling: Algorithms, Models, and Performance Analysis (2004). Chapter 42
Czumaj, A., Krysta, P., Vocking, B.: Selfish traffic allocation for server farms. In: Proc. STOC, pp. 287–296 (2002)
Czumaj, A., Vocking, B.: Tight bounds for worst-case equilibria. In: Proc. SODA, pp. 413–420 (2002)
Fleischer, L., Jain, K., Mahdian, M.: Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games. In: Proc. FOCS, pp. 277–285 (2004)
Fotakis, D., Kontogiannis, S., Koutsoupias, E., Mavronicolas, M., Spirakis, P.: The structure and complexity of Nash equilibria for a selfish routing game. In: Proc. ICALP, pp. 123–134 (2002)
Gairing, M., Lucking, T., Mavronicolas, M., Monien, B.: Computing Nash equilibria for scheduling on restricted parallel links. In: Proc. STOC, pp. 613–622 (2004)
Gairing, M., Lucking, T., Mavronicolas, M., Monien, B.: The price of anarchy for polynomial social cost. In: Proc. MFCS, pp. 574–585 (2004)
Immorlica, N., Li, L., Mirrokni, V.S., Schulz, A.: Coordination mechanisms for selfish scheduling. In: Proc. WINE, pp. 55–69 (2005)
Korilis, Y.A., Lazar, A.A., Orda, A.: Achieving network optima using Stackelberg routing strategies. IEEE/ACM Trans. Netw. 5(1), 161–173 (1997)
Koutsoupias, E.: Coordination mechanisms for congestion games. In: Sigact News, vol. 35, pp. 58–71 (2004)
Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Proc. STACS, pp. 404–413 (1999)
Koutsoupias, E., Mavronicolas, M., Spirakis, P.: Approximate equilibria and ball fusion. Theory Comput. Syst. 36(6), 683–693 (2003)
Libman, L., Orda, A.: The designer’s perspective to atomic noncooperative networks. IEEE/ACM Trans. Netw. 7(6), 875–884 (1999)
Libman, L., Orda, A.: Atomic resource sharing in noncooperative networks. Telecommun. Syst. 17(4), 385–409 (2001)
Mavronicolas, M., Spirakis, P.: The price of selfish routing. In: Proc. STOC, pp. 510–519 (2001)
Monderer, D., Shapley, L.S.: Potential games. Games Econ. Behav. 14, 124–143 (1996)
Nisan, N.: Introduction to mechanism design (for computer scientists). In: Algorithmic Game Theory, pp. 209–242. Cambridge University Press, Cambridge (2007)
Nisan, N., Ronen, A.: Algorithmic mechanism design. Games Econ. Behav. 35, 166–196 (2001)
Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)
Papadimitriou, C.H.: Algorithms, games and the Internet. In: Proc. STOC, pp. 749–753 (1999)
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2, 65–67 (1973)
Roughgarden, T.: Stackelberg scheduling strategies. In: Proc. STOC, pp. 104–113 (2001)
Roughgarden, T., Tardos, E.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)
Tardos, E., Vazirani, V.: Basic solution concepts and computational issues. In: Algorithmic Game Theory, pp. 3–28. Cambridge University Press, Cambridge (2007)
Vocking, B.: Selfish load balancing. In: Algorithmic Game Theory, pp. 517–542. Cambridge University Press, Cambridge (2007)
von Stackelberg, H.: Marktform und Gleichgewicht. Springer, Berlin (1934). English translation entitled The Theory of the Market Economy
Suri, S., Toth, C., Zhou, Y.: Selfish load balancing and atomic congestion games. In: Proc. SPAA, pp. 188–195 (2005)
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of this work appeared in the Proceedings of the 15th International Colloquium on Structural Information and Communication Complexity (SIROCCO 2008), pages 197–208, Villars-sur-Ollon, June 2008.
Rights and permissions
About this article
Cite this article
Kollias, K. Nonpreemptive Coordination Mechanisms for Identical Machines. Theory Comput Syst 53, 424–440 (2013). https://doi.org/10.1007/s00224-012-9429-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00224-012-9429-9