Constrained Coalition Formation on Valuation Structures: Formal Framework, Applications, and Islands of Tractability (Extended Abstract)

Coalition structure generation is considered in a setting where feasible coalition structures must satisfy constraints of two different kinds modeled in terms of a valuation structure, which consists of a set of pivotal agents that are pairwise incompatible, plus an interaction graph prescribing that a coalition C can form only if the subgraph induced over the nodes/agents in C is connected. It is shown that valuation structures can be used to model a number of relevant problems in real-world applications. Moreover, complexity issues arising with them are studied, by focusing in particular on identifying islands of tractability based on topological properties of the underlying interaction graph. Stability issues on valuation structures are studied too.

The Feasible Coalitional Structures in the Weighted Cooperative Games

In cooperative games, the formation of coalitional structure and their allocation are important problems. This paper firstly for participants with different position or itself by the relative inseparable coalition composition, put forward weighted cooperative game. The formations of feasible coalition structure are presented. On the basis of the revenues in all feasible coalition structures for every participant, their allocation indexes are determined and based on the allocation indexes, the revenue of the biggest coalitional structure be assigned to each participant. This method's reasonability represents that the participants' allocation indexes are from the competition among individuals and maximizing the overall revenue reflects all participants' cooperation.