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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.

Suggested Citation

  • Marco Battaglini & Salvatore Nunnari & Thomas Palfrey, 2012. "The Free Rider Problem: a Dynamic Analysis," NBER Working Papers 17926, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:17926
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    References listed on IDEAS

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    1. Marco Battaglini & Stephen Coate, 2007. "Inefficiency in Legislative Policymaking: A Dynamic Analysis," American Economic Review, American Economic Association, vol. 97(1), pages 118-149, March.
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    Citations

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    Cited by:

    1. Facundo Piguillem & Alessandro Riboni, 2015. "Spending-Biased Legislators: Discipline Through Disagreement," The Quarterly Journal of Economics, Oxford University Press, vol. 130(2), pages 901-949.
    2. Marco Battaglini & Salvatore Nunnari & Thomas R. Palfrey, 2016. "The Dynamic Free Rider Problem: A Laboratory Study," American Economic Journal: Microeconomics, American Economic Association, vol. 8(4), pages 268-308, November.
    3. Marco Battaglini & Salvatore Nunnari & Thomas R. Palfrey, 2014. "Dynamic Free Riding with Irreversible Investments," American Economic Review, American Economic Association, vol. 104(9), pages 2858-2871, September.
    4. Battaglini, Marco, 2014. "A dynamic theory of electoral competition," Theoretical Economics, Econometric Society, vol. 9(2), May.
    5. Matthews, Steven A., 2013. "Achievable outcomes of dynamic contribution games," Theoretical Economics, Econometric Society, vol. 8(2), May.
    6. Matros, Alexander & Smirnov, Vladimir, 2011. "Treasure game," Working Papers 2011-10, University of Sydney, School of Economics, revised May 2014.
    7. Giorgio Ferrari & Frank Riedel & Jan-Henrik Steg, 2013. "Continuous-Time Public Good Contribution under Uncertainty: A Stochastic Control Approach," Papers 1307.2849, arXiv.org, revised Oct 2015.
    8. Chandan Singha, 2017. "Analysing Adoption of Soil Conservation Measures by Farmers in Darjeeling District, India," Working papers 275, Centre for Development Economics, Delhi School of Economics.
    9. Chandan Singha, 2017. "Analyzing Adoption of soil Conservation Measures by Farmers in Darjeeling District, India," Working Papers id:12204, eSocialSciences.
    10. Hannu Salonen, 2012. "On Markovian Cake Sharing Problems," Discussion Papers 72, Aboa Centre for Economics.
    11. Ferrari, Giorgio & Riedel, Frank & Steg, Jan-Henrik, 2016. "Continuous-Time Public Good Contribution under Uncertainty," Center for Mathematical Economics Working Papers 485, Center for Mathematical Economics, Bielefeld University.

    More about this item

    JEL classification:

    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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