Clique games: A family of games with coincidence between the nucleolus and the Shapley value
UNIVERSAL IDENTIFIER: http://hdl.handle.net/11093/2501
EDITED VERSION: https://doi.org/10.1016/j.mathsocsci.2019.10.002
UNESCO SUBJECT: 1207.06 Teoría de Juegos
DOCUMENT TYPE: article
We introduce a new family of cooperative games for which there is coincidence between the nucleolus and the Shapley value. These so-called clique games are such that agents are divided into cliques, with the value created by a coalition linearly increasing with the number of agents belonging to the same clique. Agents can belong to multiple cliques, but for a pair of cliques, at most a single agent belongs to their intersection. Finally, if two agents do not belong to the same clique, there is at most one way to link the two agents through a chain of agents, with any two non-adjacent agents in the chain belonging to disjoint sets of cliques. We examine multiple games defined on graphs that provide a fertile ground for applications of our results.
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