Feedback strategies in the market with uncertainties

TL;DR

This paper analyzes how firms use feedback strategies to deter entry in markets with stochastic demand, employing path integral control to derive equilibrium strategies under uncertainty.

Contribution

It introduces a novel model of dynamic entry deterrence with stochastic demand and derives equilibrium strategies using path integral control methods.

Findings

Weak incumbents may reveal their type by raising prices.

Entry occurs when demand reaches a high threshold.

Incumbents mix strategies based on demand levels.

Abstract

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.