Social Choice and Welfare

, Volume 43, Issue 4, pp 925–952 | Cite as

Participation and demand levels for a joint project



We examine a voluntary participation game in public good provision in which each agent has a demand level for the public good. The agent’s demand level is the minimum level of the public good from which she can receive a positive benefit. In this game, there exists a subgame perfect Nash equilibrium at which the (Pareto) efficient allocation is achieved. The voluntary participation game may also have a subgame perfect Nash equilibrium with underprovision of the public good. However, some subgame perfect Nash equilibrium with the efficient allocation satisfies strong perfection, introduced by Rubinstein (Int J Game Theory 9:1–12, 1980), and strong perfection is satisfied only by the subgame perfect Nash equilibrium with the efficient allocation. Furthermore, all payoffs at strong perfect equilibria belong to the core of the enterprise game. By these results, we conclude that in our case, the voluntary participation problem is not as serious as the earlier studies report. We also discuss the extensibility of these results.



I am indebted to the anonymous referees for their detailed comments and suggestions. I am grateful to Koichi Tadenuma, Koji Takamiya, Noriaki Matsushima, Motohiro Sato, Toshiji Miyakawa, Florian Morath, Ryo Arawatari, and Tomomi Miyazaki for their useful discussions and suggestions. I also thank the participants in the seminars at Shinshu University, Hitotsubashi University, Yokohama National University, Okayama University, Kyoto University, Hosei University, the 66th Congress of the International Institute of Public Finance, the 2010 autumn meeting of the Japanese Economic Association, the 67th Congress of the Japanese Institute of Public Finance, and the 65th European Meeting of the Econometric Society. This research was supported by a Grant-in-Aid for Scientific Research (21730156).


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of EconomicsHosei UniversityMachidaJapan

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