Skip to main content
SpringerLink
Log in

On Proportional Allocation in Hedonic Games

  • Conference paper
  • First Online:
Algorithmic Game Theory (SAGT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10504))

Included in the following conference series:

Abstract

Proportional allocation is an intuitive and widely applied mechanism to allocate divisible resources. We study proportional allocation for profit sharing in coalition formation games. Here each agent has an impact or reputation value, and each coalition represents a joint project that generates a total profit. This profit is divided among the agents involved in the project based on their reputation. We study existence, computational complexity, and social welfare of core-stable states with proportional sharing.

Core-stable states always exist and can be computed in time \(O(m \log m)\), where m is the total number of projects. Moreover, when profits have a natural monotonicity property, there exists a reputation scheme such that the price of anarchy is 1, i.e., every core-stable state is a social optimum. However, these schemes exhibit a strong inequality in reputation of agents and thus imply a lacking fairness condition. Our main results show a tradeoff between reputation imbalance and the price of anarchy. Moreover, we show lower bounds and computational hardness results on the reputation imbalance when prices of anarchy and stability are small.

This work was done while the authors were at Saarland University. Supported by DFG Cluster of Excellence MMCI at Saarland University.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Notes

  1. 1.

    Core-stability usually means that no subset of agents wants to deviate. We recover this interpretation when we assume all coalitions \(c \in 2^V \setminus C\) have profit \(w(c) = -1\).

References

  1. 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). doi:10.1007/978-3-642-40450-4_5

    Chapter  Google Scholar 

  2. Anshelevich, E., Hoefer, M.: Contribution games in networks. Algorithmica 63(1–2), 51–90 (2012)

    Article  MathSciNet  Google Scholar 

  3. Aziz, H., Brandt, F., Seedig, H.G.: Computing desirable partitions in additively separable hedonic games. Artif. Intell. 195, 316–334 (2013)

    Article  MathSciNet  Google Scholar 

  4. Birnbaum, B., Devanur, N., Xiao, L.: Distributed algorithms via gradient descent for fisher markets. In: Proceedings of 12th Conference Electronic Commerce (EC), pp. 127–136 (2011)

    Google Scholar 

  5. Branzei, S., Larson, K.: Coalitional affinity games and the stability gap. In: Proceedings of 21st International Joint Conference on Artificial Intelligence (IJCAI), pp. 79–84 (2009)

    Google Scholar 

  6. Caragiannis, I., Voudouris, A.: Welfare guarantees for proportional allocations. Theory Comput. Syst. 59(4), 581–599 (2016)

    Article  MathSciNet  Google Scholar 

  7. Cechlárova, K.: Stable partition problem. In: Kao, M.-Y. (ed.) Encyclopedia of Algorithms, pp. 1–99. Springer, New York (2008)

    Google Scholar 

  8. Christodoulou, G., Sgouritsa, A., Tang, B.: On the efficiency of the proportional allocation mechanism for divisible resources. Theory Comput. Syst. 59(4), 600–618 (2016)

    Article  MathSciNet  Google Scholar 

  9. Deng, X., Ibaraki, T., Nagamochi, H.: Algorithmic aspects of the core of combinatorial optimization games. Math. Oper. Res. 24(3), 751–766 (1999)

    Article  MathSciNet  Google Scholar 

  10. Dreze, J., Greenberg, J.: Hedonic coalitions: optimality and stability. Econometrica 48(4), 987–1003 (1980)

    Article  MathSciNet  Google Scholar 

  11. 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). doi:10.1007/978-3-642-16170-4_16

    Chapter  Google Scholar 

  12. Hajduková, J.: Coalition formation games: a survey. Int. Game Theory Rev. 8(4), 613–641 (2006)

    Article  MathSciNet  Google Scholar 

  13. Håstad, J.: Clique is hard to approximate within \(n^{1-\varepsilon }\). Acta Math. 182(1), 105–142 (1999)

    Article  MathSciNet  Google Scholar 

  14. Hoefer, M., Wagner, L.: Designing profit shares in matching and coalition formation games. In: Chen, Y., Immorlica, N. (eds.) WINE 2013. LNCS, vol. 8289, pp. 249–262. Springer, Heidelberg (2013). doi:10.1007/978-3-642-45046-4_21

    Chapter  MATH  Google Scholar 

  15. Johari, R., Tsitsiklis, J.: Efficiency loss in a resource allocation game. Math. Oper. Res. 29(3), 407–435 (2004)

    Article  MathSciNet  Google Scholar 

  16. Kleinberg, J., Oren, S.: Mechanisms for (mis)allocating scientific credit. In: Proceedings of 43rd Symposium on Theory of Computing (STOC), pp. 529–538 (2011)

    Google Scholar 

  17. Peters, D.: Graphical hedonic games of bounded treewidth. In: Proceedings of 23rd Conference on Artificial Intelligence (AAAI), pp. 586–593 (2016)

    Google Scholar 

  18. Peters, D.: Towards structural tractability in hedonic games. In: Proceedings of 23rd Conference on Artificial Intelligence (AAAI), pp. 4252–4253 (2016)

    Google Scholar 

  19. Peters, D., Elkind, E.: Simple causes of complexity in hedonic games. In Proceedings of 24th International Joint Conference on Artificial Intelligence (IJCAI), pp. 617–623 (2015)

    Google Scholar 

  20. Shapley, L., Scarf, H.: On cores and indivisibility. J. Math. Econ. 1(1), 23–37 (1974)

    Article  MathSciNet  Google Scholar 

  21. Sung, S.-C., Dimitrov, D.: Computational complexity in additive hedonic games. Eur. J. Oper. Res. 203(3), 635–639 (2010)

    Article  MathSciNet  Google Scholar 

  22. Zhang, L.: Proportional response dynamics in the fisher market. Theor. Comput. Sci. 412(24), 2691–2698 (2011)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Computer Science, Goethe University Frankfurt, Frankfurt, Germany

    Martin Hoefer

  2. Department of Computer Science, Aalto University, Espoo, Finland

    Wanchote Jiamjitrak

Authors
  1. Martin Hoefer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wanchote Jiamjitrak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wanchote Jiamjitrak .

Editor information

Editors and Affiliations

  1. University of Salento, Lecce, Italy

    Vittorio Bilò

  2. University of L'Aquila, L'Aquila, Italy

    Michele Flammini

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Hoefer, M., Jiamjitrak, W. (2017). On Proportional Allocation in Hedonic Games. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66700-3_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66699-0

  • Online ISBN: 978-3-319-66700-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation