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The Free Rider Problem: a Dynamic Analysis

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  • Marco Battaglini
  • Salvatore Nunnari
  • Thomas Palfrey

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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 17926.

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Date of creation: Mar 2012
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Handle: RePEc:nbr:nberwo:17926

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References

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  1. Stephen Coate & Marco Battaglini, 2007. "A Dynamic Theory of Public Spending, Taxation and Debt," 2007 Meeting Papers, Society for Economic Dynamics 573, Society for Economic Dynamics.
  2. Kenji Fujiwara & Norimichi Matsueda, 2009. "Dynamic Voluntary Provision of Public Goods: A Generalization," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(1), pages 27-36, 02.
  3. Battaglini, Marco & Nunnari, Salvatore & Palfrey, Thomas, 2011. "Legislative bargaining and the dynamics of public investment," Discussion Papers, Research Unit: Market Behavior SP II 2011-205, Social Science Research Center Berlin (WZB).
  4. Fershtman, C. & Nitzan, S., 1988. "Dynamic Voluntary Provision Of Public Goods," Papers, Tel Aviv 21-88, Tel Aviv.
  5. Palfrey, Thomas R. & Rosenthal, Howard, 1984. "Participation and the provision of discrete public goods: a strategic analysis," Journal of Public Economics, Elsevier, vol. 24(2), pages 171-193, July.
  6. Marx, Leslie M & Matthews, Steven A, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 67(2), pages 327-58, April.
  7. Gaitsgory, Vladimir & Nitzan, Shmuel, 1994. "A folk theorem for dynamic games," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 167-178, March.
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Cited by:
  1. Facundo Piguillem & Alessandro Riboni, 2013. "Spending Biased Legislators - Discipline Through Disagreement," EIEF Working Papers Series 1317, Einaudi Institute for Economics and Finance (EIEF), revised Jul 2013.
  2. Giorgio Ferrari & Jan-Henrik Steg & Frank Riedel, 2013. "Continuous-Time Public Good Contribution under Uncertainty," Working Papers 485, Bielefeld University, Center for Mathematical Economics.
  3. Matthews, Steven A., 2013. "Achievable outcomes of dynamic contribution games," Theoretical Economics, Econometric Society, Econometric Society, vol. 8(2), May.
  4. Battaglini, Marco, 2011. "A Dynamic theory of electoral competition," CEPR Discussion Papers 8633, C.E.P.R. Discussion Papers.
  5. Hannu Salonen, 2012. "On Markovian Cake Sharing Problems," Discussion Papers, Aboa Centre for Economics 72, Aboa Centre for Economics.
  6. Matros, Alexander & Smirnov, Vladimir, 2011. "Treasure game," Working Papers 2011-10, University of Sydney, School of Economics.

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