Abstract
Coalition formation games model settings where sets of agents have to partition into groups. We study the notion of core stability in the context of altruistic coalition formation games (ACFGs). While in most commonly studied classes of coalition formation games agents seek to maximize their individual valuations, agents are not completely selfish in ACFGs. Given some underlying network of friendship, the agents also take into account their friends’ valuations when comparing different coalitions or coalition structures. The notion of the core has been extensively studied for several classes of (hedonic) coalition formation games. Kerkmann and Rothe [7] initiated the study of core stability in ACFGs. They showed that verifying core stability is \(\textrm{coNP}\)-complete for selfish-first ACFGs—their least altruistic case of ACFGs. The complexity of the other two (more altruistic) degrees of altruism, however, remained an open problem. We show that the core stability verification problem is \(\textrm{coNP}\)-complete for all cases of ACFGs, i.e., for all three degrees of altruism and for both sum-based and minimum-based aggregation of the friends’ preferences.
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.
The number of enemies of these friends cannot be reduced in \(\varGamma _{C\rightarrow \emptyset }\), because we have shown in Claim 3 that if any player from \( Eta \) or \( Beta \) is in C, then all of them are, or otherwise none of them is in C, but then all of them are in R as in \(\varGamma \).
References
Banerjee, S., Konishi, H., Sönmez, T.: Core in a simple coalition formation game. Soc. Choice Welfare 18(1), 135–153 (2001)
Bullinger, M., Kober, S.: Loyalty in cardinal hedonic games. In: Proceedings of the 30th International Joint Conference on Artificial Intelligence, pp. 66–72. ijcai.org (2021)
Dimitrov, D., Borm, P., Hendrickx, R., Sung, S.: Simple priorities and core stability in hedonic games. Soc. Choice Welfare 26(2), 421–433 (2006)
Gonzalez, T.: Clustering to minimize the maximum intercluster distance. Theor. Comput. Sci. 38, 293–306 (1985)
Kerkmann, A., Cramer, S., Rothe, J.: Altruism in coalition formation games. Annals Math. Artifi. Intell. (2024). https://doi.org/10.1007/s10472-023-09881-y
Kerkmann, A., et al.: Altruistic hedonic games. J. Artif. Intell. Res. 75, 129–169 (2022)
Kerkmann, A., Rothe, J.: Altruism in coalition formation games. In: Proceedings of the 29th International Joint Conference on Artificial Intelligence, pp. 347–353. ijcai.org (2020)
Munagala, K., Shen, Y., Wang, K.: Auditing for core stability in participatory budgeting. In: Hansen, K., Liu, T.X., Malekian, A. (eds.) WINE 2022. LNCS, vol. 13778, pp. 292–310. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22832-2_17
Nguyen, N., Rey, A., Rey, L., Rothe, J., Schend, L.: Altruistic hedonic games. In: Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems, pp. 251–259. IFAAMAS (2016)
Peters, D.: Precise complexity of the core in dichotomous and additive hedonic games. In: Rothe, J. (ed.) Algorithmic Decision Theory. ADT 2017. LNCS, vol. 10576, pp. 214–227. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67504-6_15
Rey, A., Rothe, J., Schadrack, H., Schend, L.: Toward the complexity of the existence of wonderfully stable partitions and strictly core stable coalition structures in enemy-oriented hedonic games. Ann. Math. Artif. Intell. 77(3), 317–333 (2016)
Rothe, J.: Thou shalt love thy neighbor as thyself when thou playest: Altruism in game theory. In: Proceedings of the 35th AAAI Conference on Artificial Intelligence, pp. 15070–15077. AAAI Press (2021)
Sung, S., Dimitrov, D.: On core membership testing for hedonic coalition formation games. Oper. Res. Lett. 35(2), 155–158 (2007)
Woeginger, G.: A hardness result for core stability in additive hedonic games. Math. Soc. Sci. 65(2), 101–104 (2013)
Acknowledgments
Supported in part by DFG grant RO-1202/21-1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Hoffjan, M., Kerkmann, A.M., Rothe, J. (2024). Core Stability in Altruistic Coalition Formation Games. In: Soto, J.A., Wiese, A. (eds) LATIN 2024: Theoretical Informatics. LATIN 2024. Lecture Notes in Computer Science, vol 14579. Springer, Cham. https://doi.org/10.1007/978-3-031-55601-2_21
Download citation
DOI: https://doi.org/10.1007/978-3-031-55601-2_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-55600-5
Online ISBN: 978-3-031-55601-2
eBook Packages: Computer ScienceComputer Science (R0)