Game of Singular Stochastic Control and Strategic Exit
Mathematics of Operations Research, 2015, Volume 40, Issue 4, 869 - 887
35 Pages Posted: 6 Jun 2014 Last revised: 9 Jan 2019
Date Written: June 4, 2014
We investigate a game of singular control and strategic exit in a model of competitive market share control. In the model, each player can make irreversible investments to increase his market share which is modeled as a diffusion process. In addition, each player has an option to exit the market at any point in time. We formulate a verification theorem for best responses of the game and characterize Markov perfect equilibria (MPE) under a set of verifiable assumptions. We find a class of MPEs with a rich structure. In particular, each player maintains up to two disconnected intervals of singular control regions, one of which plays a defensive role while the other plays an offensive role. We also identify a set of conditions under which the outcome of the game may be unique despite the multiplicity of the equilibria.
Keywords: singular control and stopping game, Markov perfect equilibrium, diffusion process
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