skip to main content
research-article

Arbitration and stability in cooperative games

Published: 25 November 2014 Publication History

Abstract

We present a formal framework for handling deviation in settings where players divide resources among multiple projects, forming overlapping coalition structures. Having formed such a coalition structure, players share the revenue generated among themselves. Given a profit division, some players may decide that they are underpaid, and deviate from the outcome. The main insight of the work presented in this survey is that when players want to deviate, they must know how the non-deviators would react to their deviation: after the deviation, the deviators may still work with some of the non-deviators, which presents an opportunity for the non-deviators to exert leverage on deviators. We extend the overlapping coalition formation (OCF) model of Chalkiadakis et al. [2010] for cooperation with partial coalitions, by introducing arbitration functions, a general framework for handling deviation in OCF games. We review some interesting aspects of the model, characterizations of stability in this model, as well as methods for computing stable outcomes.

References

[1]
Ackerman, M. and Brânzei, S. 2012. Research quality, fairness, and authorship order. CoRR abs/1208.3391.
[2]
Bachrach, Y., Elkind, E., Meir, R., Pasechnik, D., Zuckerman, M., Rothe, J., and Rosenschein, J. 2009. The cost of stability in coalitional games. In Proceedings of the 2nd International Symposium on Algorithmic Game Theory (SAGT-09). 122--134.
[3]
Bondareva, O. 1963. Some applications of linear programming methods to the theory of cooperative games. Problemy Kibernetiki 10, 119--139.
[4]
Brânzei, S., Michalak, T., Rahwan, T., Larson, K., and Jennings, N. R. 2013. Matchings with externalities and attitudes. In Proceedings of the 12th International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS-13). 295--302.
[5]
Chalkiadakis, G., Elkind, E., Markakis, E., Polukarov, M., and Jennings, N. 2010. Cooperative games with overlapping coalitions. Journal of Artificial Intelligence Research 39, 179--216.
[6]
Chalkiadakis, G., Elkind, E., and Wooldridge, M. 2011. Computational Aspects of Cooperative Game Theory. Morgan and Claypool.
[7]
Peleg, B. and Sudhölter, P. 2007. Introduction to the Theory of Cooperative Games, Second ed. Theory and Decision Library. Series C: Game Theory, Mathematical Programming and Operations Research, vol. 34. Springer, Berlin.
[8]
Shapley, L. 1967. On balanced sets and cores. Naval Research Logistics Quarterly 14, 4, 453--460.
[9]
Shapley, L. 1971. Cores of convex games. International Journal of Game Theory 1, 11--26.
[10]
Zick, Y., Chalkiadakis, G., and Elkind, E. 2012. Overlapping coalition formation games: Charting the tractability frontier. In Proceedings of the 11th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS-12). 787--794.
[11]
Zick, Y. and Elkind, E. 2011. Arbitrators in overlapping coalition formation games. In Proceedings of the 10th International Joint Conference on Autonomous agents and Multiagent Systems (AAMAS-11). 55--62.
[12]
Zick, Y., Markakis, E., and Elkind, E. 2012. Stability via convexity and LP-duality in OCF games. In Proceedings of the 26th AAAI Conference on AI (AAAI-12). 1506--1512.

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM SIGecom Exchanges
ACM SIGecom Exchanges  Volume 12, Issue 2
December 2013
53 pages
EISSN:1551-9031
DOI:10.1145/2692359
Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 November 2014
Published in SIGECOM Volume 12, Issue 2

Check for updates

Author Tags

  1. arbitration functions
  2. overlapping coalitions
  3. stability

Qualifiers

  • Research-article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 31
    Total Downloads
  • Downloads (Last 12 months)1
  • Downloads (Last 6 weeks)0
Reflects downloads up to 27 Feb 2025

Other Metrics

Citations

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media