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

See all articles by H. Dharma Kwon

H. Dharma Kwon

University of Illinois at Urbana-Champaign - Gies College of Business

Hongzhong Zhang

Columbia University

Date Written: June 4, 2014

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 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

Suggested Citation

Kwon, H. Dharma and Zhang, Hongzhong, Game of Singular Stochastic Control and Strategic Exit (June 4, 2014). Mathematics of Operations Research, 2015, Volume 40, Issue 4, 869 - 887, Available at SSRN: https://ssrn.com/abstract=2446209 or http://dx.doi.org/10.2139/ssrn.2446209

H. Dharma Kwon (Contact Author)

University of Illinois at Urbana-Champaign - Gies College of Business ( email )

1206 South Sixth Street
Champaign, IL 61820
United States

Hongzhong Zhang

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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