×

Preemption in a real option game with a first mover advantage and player-specific uncertainty. (English) Zbl 1206.91015

There are two players both of whom can invest in an project by paying a fixed cost \(I>0\). Players’ payoffs are influenced by a random shock. The shock for player \(i\) is a stochastic process \(Y_i\) which follows a geometric Brownian motion \(dY_i/Y_i=\mu dt+\sigma dz_i, Y_i(0)=y_i,\) where \(z_1\) and \(z_2\) are correlated Wiener processes. Each moment \( t\) player \(i\) obtains the discounted payoff \(e^{-rt}D_{k,l} Y_i(t)\) which depends on the investment status \(k\) of the player. Here \(k=1\) if she has invested and k=0, otherwise, and \(l\) denotes the other player’s investment status. It is assumed that \(D_{10}>D_{11}>D_{00}\geq D_{01}\) and there is a first mover advantage in that \(D_{10}-D_{00}>D_{11}-D_{01}\). This game is an extension of the model studied by Huisman and Kort (1999). It is shown that there exists an equilibrium which has different properties from those in standard real option games driven by common stochastic shocks.

MSC:

91A55 Games of timing
60G40 Stopping times; optimal stopping problems; gambling theory
91A05 2-person games
91G50 Corporate finance (dividends, real options, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Dixit, A. K.; Pindyck, R. S., Investment under Uncertainty (1994), Princeton University Press: Princeton University Press Princeton
[2] Fudenberg, D.; Tirole, J., Preemption and rent equalization in the adoption of new technology, Rev. Econ. Stud., 52, 383-401 (1985) · Zbl 0566.90014
[3] K.J.M. Huisman, P.M. Kort, Effects of strategic interactions on the option value of waiting, CentER DP No. 9992, Tilburg University, Tilburg, The Netherlands, 1999.; K.J.M. Huisman, P.M. Kort, Effects of strategic interactions on the option value of waiting, CentER DP No. 9992, Tilburg University, Tilburg, The Netherlands, 1999.
[4] Simon, L. K.; Stinchcombe, M. B., Extensive form games in continuous time: Pure strategies, Econometrica, 57, 1171-1214 (1989) · Zbl 0693.90106
[5] Thijssen, J. J.J., Irreversible investment and discounting: An arbitrage pricing approach, Ann. Finance, 6, 295-315 (2010) · Zbl 1233.91312
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.