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Continuous-Time Public Good Contribution under Uncertainty

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  • Giorgio Ferrari

    (Bielefeld University)

  • Jan-Henrik Steg

    (Bielefeld University)

  • Frank Riedel

    (Bielefeld University)

Abstract

We study a continuous-time problem of optimal public good contribution under uncertainty for an economy with a finite number of agents. Each agent can allocate his wealth between private consumption and repeated but irreversible contributions to increase the stock of some public good. We study the corresponding social planner problem and the case of strategic interaction between the agents and we characterize the optimal investment policies by a set of necessary and sufficient stochastic Kuhn-Tucker conditions. Suitably combining arguments from Duality Theory and the General Theory of Stochastic Processes, we prove an abstract existence result for a Nash equilibrium of our public good contribution game. Also, we show that our model exhibits a dynamic free rider effect. We explicitly evaluate it in a symmetric Black-Scholes setting with Cobb-Douglas utilities and we show that uncertainty and irreversibility of public good provisions do not affect free-riding.

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File URL: http://www.imw.uni-bielefeld.de/n/upload/paper/335f5352088d7d9bf74191e006d8e24c.pdf
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 485.

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Length: 34 pages
Date of creation: Jul 2013
Date of revision:
Handle: RePEc:bie:wpaper:485

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Related research

Keywords: irreversible investment; singular stochastic control; first order conditions for optimality; stochastic games; Nash equilibrium; free-riding;

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References

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  1. V. Martins-da-Rocha & Frank Riedel, 2006. "Stochastic equilibria for economies under uncertainty with intertemporal substitution," Annals of Finance, Springer, vol. 2(1), pages 101-122, January.
  2. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
  3. Jean-Jacques Laffont, 1988. "Fundamentals of Public Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121271, January.
  4. Parimal Bag & Santanu Roy, 2008. "On Sequential and Simultaneous Contributions under Incomplete Information," Departmental Working Papers 0805, Southern Methodist University, Department of Economics, revised Nov 2008.
  5. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
  6. Jan-Henrik Steg, 2009. "Irreversible investment in oligopoly," Working Papers 415, Bielefeld University, Center for Mathematical Economics.
  7. Leslie M. Marx & Steven A. Matthews, 1997. "Dynamic Voluntary Contribution to a Public Project," Discussion Papers 1188, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Maria B. Chiarolla & Giorgio Ferrari, 2011. "Identifying the Free Boundary of a Stochastic, Irreversible Investment Problem via the Bank-El Karoui Representation Theorem," Papers 1108.4886, arXiv.org, revised Dec 2013.
  9. 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.
  10. Xia Su & Frank Riedel, 2006. "On Irreversible Investment," Bonn Econ Discussion Papers bgse13_2006, University of Bonn, Germany.
  11. Lockwood, B. & Thomas, J.P., 1999. "Gradualism and Irreversibility," The Warwick Economics Research Paper Series (TWERPS) 525, University of Warwick, Department of Economics.
  12. Maria B. Chiarolla & Giorgio Ferrari & Frank Riedel, 2012. "Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources," Working Papers 463, Bielefeld University, Center for Mathematical Economics.
  13. Peter Bank & Frank Riedel, 2003. "Optimal Dynamic Choice of Durable and Perishable Goods," Bonn Econ Discussion Papers bgse29_2003, University of Bonn, Germany.
  14. Theodore Groves & John Ledyard, 1976. "Optimal Allocation of Public Goods: A Solution to the 'Free Rider Problem'," Discussion Papers 144, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Marco Battaglini & Salvatore Nunnari & Thomas Palfrey, 2012. "The Free Rider Problem: a Dynamic Analysis," NBER Working Papers 17926, National Bureau of Economic Research, Inc.
  16. Varian, Hal R., 1994. "Sequential contributions to public goods," Journal of Public Economics, Elsevier, vol. 53(2), pages 165-186, February.
  17. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
  18. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
  19. Wen-Kai Wang & Christian-Oliver Ewald, 2010. "Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model," Decisions in Economics and Finance, Springer, vol. 33(2), pages 97-116, November.
  20. Kerry Back & Dirk Paulsen, 2009. "Open-Loop Equilibria and Perfect Competition in Option Exercise Games," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4531-4552, November.
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