The Free Rider Problem: A Dynamic Analysis

50 Pages Posted: 25 Mar 2012 Last revised: 26 Dec 2021

See all articles by Marco Battaglini

Marco Battaglini

Princeton University - Department of Economics; Centre for Economic Policy Research (CEPR)

Salvatore Nunnari

Bocconi University; Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research

Thomas R. Palfrey

California Institute of Technology - Division of the Humanities and Social Sciences

Date Written: March 2012

Abstract

We present a dynamic model of free riding in which n infinitely lived agents choose between private consumption and contributions to a durable public good g. We characterize the set of continuous Markov equilibria in economies with reversibility, where investments can be positive or negative; and in economies with irreversibility, where investments are non negative and g can only be reduced by depreciation. With reversibility, there is a continuum of equilibrium steady states: the highest equilibrium steady state of g is increasing in n, and the lowest is decreasing. With irreversibility, the set of equilibrium steady states converges to a unique point as depreciation converges to zero: the highest steady state possible with reversibility. In both cases, the highest steady state converges to the efficient steady state as agents become increasingly patient. In economies with reversibility there are always non-monotonic equilibria in which g converges to the steady state with damped oscillations; and there can be equilibria with no stable steady state, but a unique persistent limit cycle.

Suggested Citation

Battaglini, Marco and Nunnari, Salvatore and Palfrey, Thomas R., The Free Rider Problem: A Dynamic Analysis (March 2012). NBER Working Paper No. w17926, Available at SSRN: https://ssrn.com/abstract=2028261

Marco Battaglini (Contact Author)

Princeton University - Department of Economics ( email )

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Princeton, NJ 08544
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Centre for Economic Policy Research (CEPR)

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United Kingdom

Salvatore Nunnari

Bocconi University

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Milan, MI 20136
Italy

Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research

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Italy

Thomas R. Palfrey

California Institute of Technology - Division of the Humanities and Social Sciences ( email )

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301A Baxter Hall
Pasadena, CA 91125
United States
626-395-4088 (Phone)
626-4432-1726 (Fax)

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