Cooperative games with overlapping coalitions
Chalkiadakis, Georgios, Elkind, Edith, Markakis, Evangelos, Polukarov, Mariya and Jennings, Nick (2010) Cooperative games with overlapping coalitions. Journal of Artificial Intelligence Research, 39, (1), 179-216.
PDF (Cooperative Games with Overlapping Coalitions (JAIR, vol 39, pp179-216, Sep. 2010))
- Accepted Version
In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions—or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure.
|Subjects:||Q Science > QA Mathematics > QA75 Electronic computers. Computer science|
|Divisions:||Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Agents, Interactions & Complexity
|Date Deposited:||20 Sep 2010 21:49|
|Last Modified:||28 Mar 2014 15:25|
Funded by: EPSRC (EP/C548051/1)
UNSPECIFIED to UNSPECIFIED
|Further Information:||Google Scholar|
|ISI Citation Count:||2|
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