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Game of Singular Stochastic Control and Strategic Exit

H. Dharma Kwon () and Hongzhong Zhang ()
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H. Dharma Kwon: Department of Business Administration, University of Illinois at Urbana–Champaign, Champaign, Illinois 61820
Hongzhong Zhang: Department of Statistics, Columbia University, New York, New York 10027

Mathematics of Operations Research, 2015, vol. 40, issue 4, 869-887

Abstract: 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, and 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 (search for similar items in EconPapers)
Date: 2015
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Handle: RePEc:inm:ormoor:v:40:y:2015:i:4:p:869-887