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Fear of the market or fear of the competitor? Ambiguity in a real options game

Author

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  • Hellmann, Tobias

    (Center for Mathematical Economics, Bielefeld University)

  • Thijssen, Jacco J.J.

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper we study a two–player investment game with a first mover advantage in continuous time with stochastic payoffs, driven by a geometric Brownian motion. One of the players is assumed to be ambiguous with max–min preferences over a strongly rectangular set of priors. We develop a strategy and equilibrium concept allowing for ambiguity and show that equilibria can be preemptive (a player invests at a point where investment is Pareto dominated by waiting) or sequential (one player invests as if she were the exogenously appointed leader). Following the standard literature, the worst–case prior for the ambiguous player if she is the second mover is obtained by setting the lowest possible trend in the set of priors. However, if the ambiguous player is the first mover, then the worst–case prior can be given by either the lowest or the highest trend in the set of priors. This novel result shows that “worst–case prior” in a setting with geometric Brownian motion and –ambiguity over the drift does not always equate to “lowest trend”.

Suggested Citation

  • Hellmann, Tobias & Thijssen, Jacco J.J., 2016. "Fear of the market or fear of the competitor? Ambiguity in a real options game," Center for Mathematical Economics Working Papers 533, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:533
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    File URL: https://pub.uni-bielefeld.de/download/2900480/2900481
    File Function: First Version, 2016
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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. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    3. Thijssen, Jacco J.J., 2010. "Preemption in a real option game with a first mover advantage and player-specific uncertainty," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2448-2462, November.
    4. Drew Fudenberg & Jean Tirole, 1985. "Preemption and Rent Equalization in the Adoption of New Technology," Review of Economic Studies, Oxford University Press, vol. 52(3), pages 383-401.
    5. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2014. "Investment timing and vertical relationships," International Journal of Industrial Organization, Elsevier, vol. 33(C), pages 110-123.
    6. Kuno J.M. Huisman & Peter M. Kort, 2015. "Strategic capacity investment under uncertainty," RAND Journal of Economics, RAND Corporation, vol. 46(2), pages 376-408, June.
    7. 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.
    8. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2007. "Irreversible investment and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 136(1), pages 668-694, September.
    9. Helen Weeds, 2002. "Strategic Delay in a Real Options Model of R&D Competition," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 729-747.
    10. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    11. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    12. Azevedo, Alcino & Paxson, Dean, 2014. "Developing real option game models," European Journal of Operational Research, Elsevier, vol. 237(3), pages 909-920.
    13. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
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    Keywords

    Real Options; Knightian Uncertainty; Worst–Case Prior; Optimal Stopping; Timing Game;

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