Steg J-H, Thijssen J. Quick or Persistent? Strategic Investment Demanding Versatility. Center for Mathematical Economics Working Papers. Vol 541. Bielefeld: Center for Mathematical Economics; 2015.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
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