Game of Singular Stochastic Control and Strategic Exit

• 成果类型: Article
• 署名作者: Kwon, H. Dharma; Zhang, Hongzhong
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0700
• 发表日期: 2015
• 页码: 869-887
• 关键词: model

摘要

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.