Optimal Coalition Structures in Cooperative Graph Games
Abstract
Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inherent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is computationally to optimize and solve such games. One prominent such language is the simple yet expressive Weighted Graph Games (WGGs) representation [14], which maintains knowledge about synergies between agents in the form of an edge weighted graph. We consider the problem of finding the optimal coalition structure in WGGs. The agents in such games are vertices in a graph, and the value of a coalition is the sum of the weights of the edges present between coalition members. The optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions. We show that finding the optimal coalition structure is not only hard for general graphs, but is also intractable for restricted families such as planar graphs which are amenable for many other combinatorial problems. We then provide algorithms with constant factor approximations for planar, minorfree and bounded degree graphs.
 Publication:

arXiv eprints
 Pub Date:
 August 2011
 arXiv:
 arXiv:1108.5248
 Bibcode:
 2011arXiv1108.5248B
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Multiagent Systems
 EPrint:
 16 pages. A short version of this paper is to appear at AAAI 2013