The possibility of efficient provision of a public good in voluntary participation games

In this study, we provide the conditions for efficient provision of a public good in a participation game in which a non-negative integer number of units of the public good can be provided. In the case in which at most one unit of the public good can be provided, we provide refinements of Nash equilibria at which agents choose only a Nash equilibrium with an efficient allocation and provide sufficient conditions for cost-sharing rules that guarantee the existence of a Nash equilibrium with an efficient allocation. In the case of a multi-unit public good, we provide a necessary and sufficient condition for the existence of a Nash equilibrium with an efficient allocation and prove that Nash equilibria are less likely to support efficient allocations if the participation of many agents is needed for efficient provision of the public good in the case of identical agents. I would like to thank Koichi Tadenuma, Yukihiro Nishimura, Toshiyuki Fujita, John Weymark, Tatsuyoshi Saijo, Takehiko Yamato, Toshiji Miyakawa, Motohiro Sato, Takashi Shimizu, Nobue Suzuki, and Dirk T. G. Rübbelke for helpful comments and suggestions. I also thank the anonymous referees for detailed comments and suggestions. This research was supported by the Japanese Economic Research Foundation and the Grand-in-Aid for Young Scientists (Start-up) from the Japan Society for the Promotion of Science. Any remaining errors are my own.