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Quick or Persistent? Strategic Investment Demanding Versatility

Author

Listed:
  • Steg, Jan-Henrik

    (Center for Mathematical Economics, Bielefeld University)

  • Thijssen, Jacco

    (Center for Mathematical Economics, Bielefeld University)

Abstract
In this paper we analyse a dynamic model of investment under uncertainty in a duopoly, in which each firm has an option to switch from the present market to a new market. We construct a subgame perfect equilibrium in mixed strategies and show that both preemption and attrition can occur along typical equilibrium paths. In order to determine the attrition region a two-dimensional constrained optimal stopping problem needs to be solved, for which we characterize the non-trivial stopping boundary in the state space. We explicitly determine Markovian equilibrium stopping rates in the attrition region and show that there is always a positive probability of eventual preemption, contrasting the deterministic version of the model. A simulation-based numerical example illustrates the model and shows the relative likelihoods of investment taking place in attrition and preemption regions.

Suggested Citation

  • Steg, Jan-Henrik & Thijssen, Jacco, 2015. "Quick or Persistent? Strategic Investment Demanding Versatility," Center for Mathematical Economics Working Papers 541, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:541
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    File URL: https://pub.uni-bielefeld.de/download/2757310/2757311
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    References listed on IDEAS

    as
    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. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    3. Drew Fudenberg & Jean Tirole, 1985. "Preemption and Rent Equalization in the Adoption of New Technology," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(3), pages 383-401.
    4. Grzegorz Pawlina & Peter M. Kort, 2006. "Real Options in an Asymmetric Duopoly: Who Benefits from Your Competitive Disadvantage?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(1), pages 1-35, March.
    5. Helen Weeds, 2002. "Strategic Delay in a Real Options Model of R&D Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 729-747.
    6. Pauli Murto, 2004. "Exit in Duopoly Under Uncertainty," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 111-127, Spring.
    7. Azevedo, Alcino & Paxson, Dean, 2014. "Developing real option game models," European Journal of Operational Research, Elsevier, vol. 237(3), pages 909-920.
    8. Huisman, K.J.M. & Kort, P.M., 1999. "Effects of Strategic Interactions on the Option Value of Waiting," Other publications TiSEM a867e9f4-7840-4335-83df-e, Tilburg University, School of Economics and Management.
    9. repec:fth:tilbur:9992 is not listed on IDEAS
    10. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-680, November.
    11. Boyer, Marcel & Lasserre, Pierre & Mariotti, Thomas & Moreaux, Michel, 2004. "Preemption and rent dissipation under price competition," International Journal of Industrial Organization, Elsevier, vol. 22(3), pages 309-328, March.
    12. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-960, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2019. "Dynamic competition and intellectual property rights in a model of product development," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 270-296.
    2. Steg, Jan-Henrik, 2018. "Preemptive investment under uncertainty," Games and Economic Behavior, Elsevier, vol. 110(C), pages 90-119.
    3. Lavrutich, Maria, 2016. "Strategic real options : Entry deterrence and exit inducement," Other publications TiSEM a83e0597-6450-4df7-a1e6-7, Tilburg University, School of Economics and Management.
    4. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    5. Lavrutich, Maria N., 2017. "Capacity choice under uncertainty in a duopoly with endogenous exit," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1033-1053.
    6. Steg, Jan-Henrik, 2015. "Symmetric equilibria in stochastic timing games," Center for Mathematical Economics Working Papers 543, Center for Mathematical Economics, Bielefeld University.

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    More about this item

    Keywords

    two-dimensional optimal stopping.; Markovperfect equilibrium; real options; war of attrition; preemption; Stochastic timing games;
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