Strategic Complementarity in the Dynamic Private Provision of a Discrete Public Good

• DOI: http://doi.org/10.1111/j.1467-9779.2007.00326.x
• Author: SEBASTIAN G. KESSING
• Date: 01 August 2007
• Published date: 01 August 2007

STRATEGIC COMPLEMENTARITY IN THE DYNAMIC PRIVATE

PROVISION OF A DISCRETE PUBLIC GOOD

SEBASTIAN G. KESSING

WZB and Free University Berlin

Abstract

Individual voluntary contributions to a discrete public good

are shown to be strategic complements in a dynamic private

provision game. This is in contrast to a public good that can

take on any value in a continuum where they are strategic

substitutes.

1. Introduction

The private provision of a discrete public good is characterized by the fact

that individuals will derive utility from the public good only after a certain

threshold level of overall contributions has been reached and the good is

completed. This contrasts with a continuously divisible public good which

generates utility at any provision level. This note illustrates a structural differ-

ence between the private provision of these different kinds of public goods

in dynamic differential game settings. Fershtman and Nitzan (1991) show

that individual contributions are strategic substitutes in the dynamic contri-

bution to a continuously divisible public good. I show that, in the case of a

dynamic game of private contributions to a discrete public good, individual

contributions are strategic complements.

I study a simple dynamic model of a discrete public good that has to be

completed by private contributions and may be epitomized by the proverbial

example of the building of a bridge by a group of people. Benefits only start

flowing once the bridge is completed. No agent can be excluded from the

benefits of the project and side payments are not allowed. All players have

Sebastian G. Kessing, WZB and Free University Berlin, WZB/MPS, Reichpietschufer 50,

10785 Berlin, Germany (kessing@wz-berlin.de).

I would like to thank Giuseppe Bertola, Kai Konrad, Johannes M¨unster, members of

the microeconomics workshop of the Free University, Humboldt-University and WZB, the

anonymous referees and an anonymous associate editor for their comments.

Received March 17, 2004; Accepted January 27, 2006.

C

2007 Blackwell Publishing, Inc.

Journal of Public Economic Theory,9(4), 2007, pp. 699–710.

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