Non-emptiness of the core of mcst games with revenues

Identificador:  imarina:9514366

Handle: https://hdl.handle.net/20.500.11797/imarina9514366

Autors:  Subiza, Begona; Gimenez-Gomez, Jose-Manuel; Peris, Josep E

Resum:
The minimum cost spanning tree (mcst) problem analyzes how to efficiently connect geographically dispersed agents to a common source. Est & eacute;vez-Fern & aacute;ndez and Reijnierse (2014) study mcst problems involving revenues, in which the agents benefit from being connected to the source. A key feature of their framework is that only certain coalitions, called effective coalitions, make sense to form. Est & eacute;vez-Fern & aacute;ndez and Reijnierse (2014) show that the core in cost-revenue mcst games is typically empty. In this paper, we present a necessary condition that mcst games with revenues need to fulfill to ensure the non-emptiness of the core: the existence of at least one agent with veto power, i.e., an agent whose participation is required in every effective coalition. Additionally, we extend the sufficient condition in Est & eacute;vez-Fern & aacute;ndez and Reijnierse (2014) for elementary cost mcst problems.