Game of singular stochastic control and strategic exit

Hyok-Jon Dharma Kwon, Hongzhong Zhang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)869-887
Number of pages19
JournalMathematics of Operations Research
Issue number4
StatePublished - Nov 2015


  • Diffusion process
  • Markov perfect equilibrium
  • Singular control and stopping game

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research


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