Stochastic Switching Games
| Title: | Stochastic Switching Games |
|---|---|
| Authors: | Li, Liangchen, Ludkovski, Michael |
| Publication Year: | 2018 |
| Collection: | Quantitative Finance |
| Subject Terms: | Economics - General Economics, 91A15, 91B52, 93E20, 62L15 |
| More Details: | 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. |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/1807.03893 |
| Accession Number: | edsarx.1807.03893 |
| Database: | arXiv |
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