Restricted bargaining sets in a club economy

The core as a solution concept captures the set of allocations against which there exists no objection by any coalition of agents. Aumann and Maschler (1961) however emphasized the shortcomings of the objection mechanism and hence the core to further repercussions from agents. In that spirit, they introduced the bargaining set which later was adapted to the case of exchange economies by Mas-Colell (1989) and Vind (1992). In this paper, we consider a club economy where club goods are consumed parallel to private goods to capture the social aspects of consumption. We consider the framework proposed by Ellickson et al. (1999) in this regard and refer to the bargaining sets introduced in line with Mas-Colell and Vind as the local and global bargaining sets in our framework. We provide characterizations of the global bargaining set in terms of the size of the (counter-) objecting coalitions thereby extending the works of Schødt and Sloth (1994) and Herves- Estvez and Moreno-Garcıa (2015). We provide further interpretations of the global bargaining set in terms of several notions of robustly efficient states of a club economy.