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Irreversible investment in oligopoly

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  • Jan-Henrik Steg

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Abstract

We offer a new perspective on games of irreversible investment under uncertainty in continuous time. The basis is a particular approach to solve the involved stochastic optimal control problems which allows to establish existence and uniqueness of an oligopolistic open loop equilibrium in a very general framework without reliance on any Markovian property. It simultaneously induces quite natural economic interpretation and predictions by its characterization of optimal strategies through first order conditions. The construction of equilibrium policies is then enabled by a stochastic representation theorem. A stepwise specification of the general model leads to further economic conclusions. We obtain explicit solutions for Lévy processes.

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File URL: http://hdl.handle.net/10.1007/s00780-011-0168-6
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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 16 (2012)
Issue (Month): 2 (April)
Pages: 207-224

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Handle: RePEc:spr:finsto:v:16:y:2012:i:2:p:207-224

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Related research

Keywords: Irreversible investment; Oligopoly; Equilibrium; Singular stochastic control; 60G40; 91A15; 91A25; 93E20; C73; D43; D92;

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References

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  1. 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.
  2. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
  3. Steven R. Grenadier, 2002. "Option Exercise Games: An Application to the Equilibrium Investment Strategies of Firms," Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 691-721.
  4. Pindyck, Robert S., 1986. "Irreversible investment, capacity choice, and the value of the firm," Working papers 1802-86., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  5. Novshek, William, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 85-98, January.
  6. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
  7. A. Michael Spence, 1979. "Investment Strategy and Growth in a New Market," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 1-19, Spring.
  8. Bertola, Giuseppe, 1998. "Irreversible investment," Research in Economics, Elsevier, vol. 52(1), pages 3-37, March.
  9. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
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Citations

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Cited by:
  1. Thijssen, Jacco J.J. & Huisman, Kuno J.M. & Kort, Peter M., 2012. "Symmetric equilibrium strategies in game theoretic real option models," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 219-225.
  2. Giorgio Ferrari, 2012. "On an Integral Equation for the Free-Boundary of Stochastic, Irreversible Investment Problems," Papers 1211.0412, arXiv.org, revised Jul 2013.
  3. Steg, Jan-Henrik, 2013. "Strategic Capital Accumulation with Singular Control," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79948, Verein für Socialpolitik / German Economic Association.
  4. Giorgio Ferrari & Frank Riedel & Jan-Henrik Steg, 2013. "Continuous-Time Public Good Contribution under Uncertainty," Papers 1307.2849, arXiv.org.
  5. Giorgio Ferrari, 2012. "On an Integral Equation for the Free Boundary of Stochastic, Irreversible Investment Problems," Working Papers 471, Bielefeld University, Center for Mathematical Economics.
  6. Huisman, K.J.M. & Kort, P.M., 2013. "Strategic Capacity Investment Under uncertainty," Discussion Paper 2013-003, Tilburg University, Center for Economic Research.

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