Symmetric Equilibrium Strategies in Game Theoretic Real Option Models

This paper considers the problem of investment timing under uncertainty in a duopoly framework. When both firms want to be the first investor a coordination problem arises. Here, a method is proposed to deal with this coordination problem, involving the use of symmetric mixed strategies. The method is based on Fudenberg and Tirole (1985, Review of Economic Studies), where it was designed within a deterministic framework. The aim of our paper is to extend the applicability of this method to a stochastic environment. The need for this is exemplified by the fact that several recent contributions in multiple firm real option models make unsatisfactory assumptions to solve the coordination problem mentioned above. Moreover, our approach allows us to show that in many cases it is incorrect to claim that ”the probability that both firms invest simultaneously, while it is only optimal for one firm to invest, is zero”. The authors thank Dolf Talman, Eric van Damme, participants of the Seventh Viennese Workshop on Optimal Control, Dynamic Games and Non-linear Dynamics, and seminar participants at CentER for their constructive comments. Corresponding author. Department of Econometrics & Operations Research and CentER, Tilburg University, Tilburg, PO Box 90153, 5000 LE Tilburg, The Netherlands. Tel: +31-13-4662824; fax: +31-13-4663280; e-mail: [email protected]. Centre for Quantitative Methods, PO Box 414, 5600 AK Eindhoven, The Netherlands. Department of Econometrics & Operations Research and CentER, Tilburg University, Tilburg, The Netherlands, and Department of Economics, UFSIA, University of Antwerp, Antwerp, Belgium.