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Game of Singular Stochastic Control and Strategic Exit

H. Dharma Kwon, University of Illinois at Urbana-Champaign - Department of Business Administration
Hongzhong Zhang, Columbia University - Department of Statistics


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H. DHARMA KWON, University of Illinois at Urbana-Champaign - Department of Business Administration
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HONGZHONG ZHANG, Columbia University - Department of Statistics
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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.

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