2024/10/21 by Issah, Mustapha Nyenye
#93E03 #93E20 #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Theoretical Economics (econ.TH)
paper · doi:10.48550/arxiv.2410.16203
We explore how dynamic entry deterrence operates through feedback strategies in markets experiencing stochastic demand fluctuations. The incumbent firm, aware of its own cost structure, can deter a potential competitor by strategically adjusting prices. The potential entrant faces a one-time, irreversible decision to enter the market, incurring a fixed cost, with profits determined by market conditions and the incumbent's hidden type. Market demand follows a Chan-Karolyi-Longstaff-Sanders Brownian motion. If the demand is low, the threat of entry diminishes, making deterrence less advantageous. In equilibrium, a weak incumbent may be incentivized to reveal its type by raising prices. We derive an optimal equilibrium using path integral control, where the entrant enters once demand reaches a high enough level, and the weak incumbent mixes strategies between revealing itself when demand is sufficiently low.