The equivalence of the cost share equilibria and the core of a voting game in a public goods economy

We consider a social situation where individuals choose one or some alternative(s) from a set of feasible alternatives. When one alternative is socially chosen, each individual must share the cost for it according to an exogenously given sharing rule. Individuals are allowed to collude among themselves through money transfers. As the mechanism of choosing a social alternative, we consider the cost share equilibrium and a voting game. The cost share equilibrium is an allocation where each individual maximizes his/her utility independently and where unanimity is still maintained. We will show the equivalence between the set of all equilibrium allocations and the core of the voting game with compensation.I would like to thank Professors Mamoru Kaneko, Kotaro Suzumura, William Thomson, Mikio Nakayama, Hiroo Sasaki, Mr. Ken-ichi Shimomura and anonymous referees for their many useful suggestions and comments. I also acknowledge grammatical suggestions of Mr. Ronald M. Siani.