Abstract
Job scheduling on parallel machines is a well-studied singleton congestion game. We consider a variant of this game in which the jobs are partitioned into competition sets, and the goal of every player is to minimize the completion time of his job relative to his competitors. Specifically, the primary goal of a player is to minimize the rank of its completion time among his competitors, while minimizing the completion time itself is a secondary objective. This fits environments with strong competition among the participants, in which the relative performance of the players determine their welfare.
We define and study the corresponding race scheduling game (RSG). We show that RSGs are significantly different from classical job-scheduling games, and that competition may lead to a poor outcome. In particular, an RSG need not have a pure Nash equilibrium, and best-response dynamics may not converge to a NE even if one exists. We identify several natural classes of games, on identical and on related machines, for which a NE exists and can be computed efficiently, and we present tight bounds on the equilibrium inefficiencies. For some classes we prove convergence of BRD, while for others, even with very limited competition, BRD may loop. Among classes for which a NE is not guaranteed to exist, we distinguish between classes for which, it is tractable or NP-hard to decide if a given instance has a NE.
Striving for stability, we also study the Nashification cost of RSGs, either by adding dummy jobs, or by compensating jobs for having high rank. Our analysis provides insights and initial results for several other congestion and cost-sharing games that have a natural ‘race’ variant.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In this paper, we only consider pure strategies.
References
Anagnostopoulos, A., Becchetti, L., de Keijzer, B., Schäfer, G.: Inefficiency of games with social context. Theory Comput. Syst. 57(3), 782–804 (2014). https://doi.org/10.1007/s00224-014-9602-4
Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)
Avni, G., Tamir, T.: Cost-sharing scheduling games on restricted unrelated machines. Theoret. Comput. Sci. 646, 26–39 (2016)
Aumann, R.J.: Rule-Rationality Versus Act-Rationality. Discussion Paper Series DP497, The Hebrew University’s Center for the Study of Rationality (2008)
Bilò, V., Celi, A., Flammini, M., Gallotti, V.: Social context congestion games. In: Proceedings of 18th SIROCCO, pp. 282–293 (2011)
Bolton, G.E., Ockenfels, A.: ERC: a theory of equity, reciprocity, and competition. Am. Econ. Rev. 90(1), 166–193 (2000)
Bhawalkar, K., Gairing, M., Roughgarden, T.: Weighted congestion games: the price of anarchy, universal worst-case examples, and tightness. ACM Trans. Econ. Comput. 2(4), Article 14 (2014)
Chen, P.A., de Keijzer, B., Kempe, D., Schäfer, G.: The robust price of anarchy of altruistic games. In: Proceedings of 7th WINE, pp. 383–390 (2011)
Cho, Y., Sahni, S.: Bounds for list schedules on uniform processors. SIAM J. Comput. 9(1), 91–103 (1980)
Czumaj, A., Vöcking, B.: Tight bounds for worst-case equilibria. ACM Trans. Algorithms 3(1), 4:1–4:17 (2007)
Fehr, E., Schmidt, K.M.: A theory of fairness, competition, and cooperation. Q. J. Econ. 114(3), 817–868 (1999)
Fiat, A., Kaplan, H., Levi, M., Olonetsky, S.: Strong price of anarchy for machine load balancing. In: Proceedings of 34th ICALP (2007)
Finn, G., Horowitz, E.: A linear time approximation algorithm for multiprocessor scheduling. BIT Numer. Math. 19(3), 312–320 (1979)
Fotakis, D., Kontogiannis, S., Koutsoupias, E., Mavronicolas, M., Spiraklis, P.: The structure and complexity of Nash equilibria for a selfish routing game. In: Proceedings of 29th ICALP, pp. 510–519 (2002)
Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45, 1563–1581 (1966)
Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 263–269 (1969)
Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: practical and theoretical results. J. ACM 34(1), 144–162 (1987)
Jansen, K., Klein, K.M., Verschae, J.: Closing the gap for makespan scheduling via sparsification techniques. In: Proceedings of 43rd ICALP, pp. 1–13 (2016)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. Comput. Sci. Rev. 3(2), 65–69 (2009)
Pinedo, M.: Scheduling: Theory, Algorithms, and Systems. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-642-46773-8_5
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2, 65–67 (1973)
Rosner, S., Tamir, T.: Race Scheduling Games. https://cs.idc.ac.il/~tami/Papers/RSG-full.pdf
Schulz, A.S., Stier Moses, N.: On the performance of user equilibria in traffic networks. In: Proceedings of 43rd SODA, pp. 86–87 (2003)
Vöcking, B.: Selfish load balancing. In: Algorithmic Game Theory. Chapter 20, Cambridge University Press (2007)
Winter, E., Méndez-Naya, L., García-Jurado, I.: Mental equilibrium and strategic emotions. Manage. Sci. 63(5), 1302–1317 (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Rosner, S., Tamir, T. (2020). Race Scheduling Games. In: Harks, T., Klimm, M. (eds) Algorithmic Game Theory. SAGT 2020. Lecture Notes in Computer Science(), vol 12283. Springer, Cham. https://doi.org/10.1007/978-3-030-57980-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-57980-7_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-57979-1
Online ISBN: 978-3-030-57980-7
eBook Packages: Computer ScienceComputer Science (R0)