Constrained coalition formation on valuation structures: Formal framework, applications, and islands of tractability

It is shown that valuation structures can be used to model a number of relevant problems arising in real-world application domains. Then, the complexity of coalition structure generation over valuation structures is studied, by assuming that the functions associating each coalition with its worth are given as input according to some compact encoding-rather than explicitly listing all exponentially-many associations. In particular, islands of tractability are identified based on the topological properties of the underlying interaction graphs and on suitable algebraic properties of the given worth functions. Finally, stability issues over valuation structures are studied too, by considering the core as the prototypical solution concept.