2015/06/15 by Steg, Jan-Henrik, Thijssen, Jacco
#60G40 #91A25 #91A55 #91A60 #FOS: Economics and business #FOS: Mathematics #General Economics (econ.GN) #Optimization and Control (math.OC) #Probability (math.PR)
paper · doi:10.48550/arxiv.1506.04698
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.