2018/07/10 by Liangchen Li, Michael Ludkovski, Li, Liangchen +1
Economics, Econometrics and Finance · #Capital Investment and Risk Analysis #Economic theories and models #Stochastic processes and financial applications #econ.GN #msc:62L15 #msc:91A15 #msc:91B52 #msc:93E20 #q-fin.EC
paper · pdf · doi:10.48550/arxiv.1807.03893
arxiv created 2018/07/10 · arxiv updated 2018/07/23
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^∗ and a Geometric Brownian Motion X that makes M^∗ eventually "absorbed" as one player eventually gains permanent advantage. Explicit computations and comparative statics regarding the emergent macroscopic market equilibrium are also provided.