Committee-structured games in a cooperative framework

Abstract

We introduce the notion of committee-structured games (CSG) in a cooperative framework to analyze situations where committees affect players in generating their coalitional values. We represent the sets of committees by hypergraphs and obtain values as a function of both coalitions and hypergraphs. Based on how committee structures affect value generation, we present two models within the CSG framework. In the first model, the total value is generated by the committee set as a whole, while in the second model, it is obtained by aggregating contributions from all subsets of the set of committees. Accordingly, we define the Shapley value for the first model and the Aggregated Shapley value for the second, providing axiomatic characterizations for both. Further, we propose bidding mechanisms to show that the Shapley value and the Aggregated Shapley value for the class of CSG is a subgame perfect Nash equilibrium (SPNE) of the induced strategic game. Finally, we study an alternative Exchange Economy model by incorporating committees instead of commodities