Abstract
Matching and coalition formation are fundamental problems in a variety of scenarios where agents join efforts to perform tasks, such as, e.g., in scientific publishing. To allocate credit or profit stemming from a joint project, different communities use different crediting schemes in practice. A natural and widely used approach to profit distribution is equal sharing, where every member receives the same credit for a joint work. This scheme captures a natural egalitarian fairness condition when each member of a coalition is critical for success. Unfortunately, when coalitions are formed by rational agents, equal sharing can lead to high inefficiency of the resulting stable states.
In this paper, we study the impact of changing profit sharing schemes in order to obtain good stable states in matching and coalition formation games. We generalize equal sharing to sharing schemes where for each coalition each player is guaranteed to receive at least an α-share. This way the coalition formation can stabilize on more efficient outcomes. In particular, we show a direct trade-off between efficiency and equal treatment. If k denotes the size of the largest possible coalition, we prove an asymptotically tight bound of k 2 α on prices of anarchy and stability. This result extends to polynomial-time algorithms to compute good sharing schemes. Further, we show improved results for a novel class of matching problems that covers many well-studied cases, including two-sided matching and instances with integrality gap 1.
Supported by DFG Cluster of Excellence MMCI and grant Ho 3831/3-1.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ackermann, H., Goldberg, P., Mirrokni, V., Röglin, H., Vöcking, B.: Uncoordinated two-sided matching markets. SIAM J. Comput. 40(1), 92–106 (2011)
Akkaya, K., Guneydas, I., Bicak, A.: Autonomous actor positioning in wireless sensor and actor networks using stable matching. Intl. J. Parallel, Emergent and Distrib. Syst. 25(6), 439–464 (2010)
Anshelevich, E., Bhardwaj, O., Hoefer, M.: Friendship and stable matching. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 49–60. Springer, Heidelberg (2013)
Anshelevich, E., Das, S., Naamad, Y.: Anarchy, stability, and utopia: Creating better matchings. Auton. Agents Multi-Agent Syst. 26(1), 120–140 (2013)
Anshelevich, E., Hoefer, M.: Contribution games in networks. Algorithmica 63(1-2), 51–90 (2012)
Augustine, J., Chen, N., Elkind, E., Fanelli, A., Gravin, N., Shiryaev, D.: Dynamics of profit-sharing games. In: Proc. 22nd Intl. Joint Conf. Artif. Intell. (IJCAI), pp. 37–42 (2011)
Biró, P., Kern, W., Paulusma, D.: Computing solutions for matching games. Int. J. Game Theory 41(1), 75–90 (2011)
Blum, Y., Roth, A., Rothblum, U.: Vacancy chains and equilibration in senior-level labor markets. J. Econom. Theory 76, 362–411 (1997)
Branzei, S., Larson, K.: Coalitional affinity games and the stability gap. In: Proc. 21st Intl. Joint Conf. Artif. Intell. (IJCAI), pp. 79–84 (2009)
Cechlárova, K.: Stable partition problem. In: Encyclopedia of Algorithms (2008)
Chen, H.-L., Roughgarden, T., Valiant, G.: Designing network protocols for good equilibria. SIAM J. Comput. 39(5), 1799–1832 (2010)
Chen, N., Lu, P., Zhang, H.: Computing the nucleolus of matching, cover and clique games. In: Proc. 26th Conf. Artificial Intelligence, AAAI (2012)
Deng, X., Ibaraki, T., Nagamochi, H.: Algorithmic aspects of the core of combinatorial optimization games. Math. Oper. Res. 24(3), 751–766 (1999)
Gairing, M., Savani, R.: Computing stable outcomes in hedonic games. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 174–185. Springer, Heidelberg (2010)
Gusfield, D., Irving, R.: The Stable Marriage Problem: Structure and Algorithms. MIT Press (1989)
Hajduková, J.: Coalition formation games: A survey. Intl. Game Theory Rev. 8(4), 613–641 (2006)
Hoefer, M.: Local matching dynamics in social networks. Inf. Comput. 222, 20–35 (2013)
Hoefer, M., Wagner, L.: Locally stable marriage with strict preferences. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 620–631. Springer, Heidelberg (2013)
Kern, W., Paulusma, D.: Matching games: The least core and the nucleolus. Math. Oper. Res. 28(2), 294–308 (2003)
Kleinberg, J., Oren, S.: Mechanisms for (mis)allocating scientific credit. In: Proc. 43rd Symp. Theory of Computing (STOC), pp. 529–538 (2011)
Kleinberg, J., Tardos, É.: Balanced outcomes in social exchange networks. In: Proc. 40th Symp. Theory of Computing (STOC), pp. 295–304 (2008)
Manlove, D.: Algorithmics of Matching Under Preferences. World Scientific (2013)
Sung, S.-C., Dimitrov, D.: Computational complexity in additive hedonic games. Europ. J. Oper. Res. 203(3), 635–639 (2010)
von Falkenhausen, P., Harks, T.: Optimal cost sharing for resource selection games. Math. Oper. Res. 38(1), 184–208 (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hoefer, M., Wagner, L. (2013). Designing Profit Shares in Matching and Coalition Formation Games. In: Chen, Y., Immorlica, N. (eds) Web and Internet Economics. WINE 2013. Lecture Notes in Computer Science, vol 8289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45046-4_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-45046-4_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45045-7
Online ISBN: 978-3-642-45046-4
eBook Packages: Computer ScienceComputer Science (R0)