The Olson Conjecture for Discrete Public Goods

29 Pages Posted: 18 Dec 2018

See all articles by Georg Nöldeke

Georg Nöldeke

University of Basel; University of Basel

Jorge Peña

Institute for Advanced Study in Toulouse

Date Written: November 29, 2018

Abstract

We consider the private provision of a public good with non-refundable binary contributions.

A fixed amount of the good is provided if and only if the number of contributors reaches an exogenous threshold. The threshold, the group size, and the identical cost of contributing to the public good are common knowledge. Our main result shows that the maximal probability of reaching the threshold (and thereby obtaining the public good) which can be supported in a symmetric equilibrium of this participation game is decreasing in group size. This generalizes a well-known result for the volunteer's dilemma -- in which the threshold is one -- to arbitrary thresholds and thereby confirms a conjecture by Olson for the class of participation games under consideration. Further results characterize the limit when group size goes to infinity and provide conditions under which the expected number of contributors is decreasing or increasing in group size.

Keywords: Participation games, Private provision of public goods, Group-size effects, Olson conjecture

JEL Classification: C72, D71, H41

Suggested Citation

Nöldeke, Georg and Peña, Jorge, The Olson Conjecture for Discrete Public Goods (November 29, 2018). Available at SSRN: https://ssrn.com/abstract=3292976 or http://dx.doi.org/10.2139/ssrn.3292976

Georg Nöldeke (Contact Author)

University of Basel ( email )

Peter Merian-Weg 6
Basel, 4002
Switzerland

HOME PAGE: http://sites.google.com/site/georgnoldeke/

University of Basel ( email )

Peter Merian-Weg 6
Basel, 4002
Switzerland

HOME PAGE: http://sites.google.com/site/georgnoldeke/

Jorge Peña

Institute for Advanced Study in Toulouse ( email )

31015 Toulouse, Cedex 6
France

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