Clique games: A family of games with coincidence between the nucleolus and the Shapley value

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.Social Sciences and Humanities Research Council of Canada | Ref. 435-2014-0140Agencia Estatal de Investigación | Ref. ECO2017-82241-RMinisterio de Economía y Competitividad | Ref. ECO2014-52616-RXunta de Galicia | Ref. GRC 2015/01