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Continuous-Time Public Good Contribution under Uncertainty

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

  • Steg, Jan-Henrik

    (Center for Mathematical Economics, Bielefeld University)

We study a continuous-time problem of optimal public good contribution under uncertainty for an economy with an 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: https://pub.uni-bielefeld.de/download/2674160/2674161
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Paper provided by Center for Mathematical Economics, Bielefeld University in its series Center for Mathematical Economics Working Papers with number 485.

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Date of creation: 30 Apr 2014
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Handle: RePEc:bie:wpaper:485
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  1. Ferrari, Giorgio, 2014. "On an integral equation for the free boundary of stochastic, irreversible investment problems," Center for Mathematical Economics Working Papers 471, Center for Mathematical Economics, Bielefeld University.
  2. Parimal Bag & Santanu Roy, 2011. "On sequential and simultaneous contributions under incomplete information," International Journal of Game Theory, Game Theory Society, vol. 40(1), pages 119-145, February.
  3. Lockwood, B. & Thomas, J.P., 1999. "Gradualism and Irreversibility," The Warwick Economics Research Paper Series (TWERPS) 550, University of Warwick, Department of Economics.
  4. Eve Chiapello & A. Hurand, 2011. "Contribution," Post-Print hal-00681170, HAL.
  5. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
  6. V. Filipe Martins-da-Rocha & Frank Riedel, 2008. "On Equilibrium Prices in Continuous Time," Papers 0802.3585, arXiv.org.
  7. Varian, Hal R., 1994. "Sequential contributions to public goods," Journal of Public Economics, Elsevier, vol. 53(2), pages 165-186, February.
  8. Chiarolla, Maria B. & Ferrari, Giorgio & Riedel, Frank, 2014. "Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources," Center for Mathematical Economics Working Papers 463, Center for Mathematical Economics, Bielefeld University.
  9. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
  10. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May.
  11. 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.
  12. 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.
  13. Marco Battaglini & Salvatore Nunnari & Thomas Palfrey, 2012. "The Free Rider Problem: a Dynamic Analysis," NBER Working Papers 17926, National Bureau of Economic Research, Inc.
  14. Peter Bank & Frank Riedel, 2003. "Optimal Dynamic Choice of Durable and Perishable Goods," Bonn Econ Discussion Papers bgse29_2003, University of Bonn, Germany.
  15. 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.
  16. 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.
  17. 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.
  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. Leslie M. Marx & Steven A. Matthews, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 327-358.
  20. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
  21. Jan-Henrik Steg, 2012. "Irreversible investment in oligopoly," Finance and Stochastics, Springer, vol. 16(2), pages 207-224, April.
  22. Jean-Jacques Laffont, 1988. "Fundamentals of Public Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121271, March.
  23. Cornes,Richard & Sandler,Todd, 1996. "The Theory of Externalities, Public Goods, and Club Goods," Cambridge Books, Cambridge University Press, number 9780521477185, November.
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