Stochastic Switching Games

• Tác giả: Liangchen Li, Michael Ludkovski
• Ngôn ngữ: eng
• Ký hiệu phân loại: 003.76 Stochastic systems
• Thông tin xuất bản: 2018
• Bộ sưu tập: Metadata
• ID: 162059

Tóm tắt

We study nonzero-sum stochastic switching games. Two players compete for market dominance through controlling (via timing options) the discrete-state market regime $M$. Switching decisions are driven by a continuous stochastic factor $X$ that modulates instantaneous revenue rates and switching costs. This generates a competitive feedback between the short-term fluctuations due to $X$ and the medium-term advantages based on $M$. We construct threshold-type Feedback Nash Equilibria which characterize stationary strategies describing long-run dynamic equilibrium market organization. Two sequential approximation schemes link the switching equilibrium to (i) constrained optimal switching, (ii) multi-stage timing games. We provide illustrations using an Ornstein-Uhlenbeck $X$ that leads to a recurrent equilibrium $M^\ast$ and a Geometric Brownian Motion $X$ that makes $M^\ast$ eventually "absorbed" as one player eventually gains permanent advantage. Explicit computations and comparative statics regarding the emergent macroscopic market equilibrium are also provided.