Dynamic Pricing and Risk Analytics Under Competition and Stochastic Reference Price Effects

This paper investigates the pricing strategy of firms in the context of uncertain demand. In particular, there are two factors that affect demand dynamics, the influence of reference prices and the price of the competition. In the monopoly case, pricing policy is affected by reference-price effects and in the duopoly case, both competitive pricing and reference-price effects are present. In each case, the optimal price paths are derived and simulated. The implications of uncertainty are analyzed by comparing the deterministic policy with the stochastic policy. The random variations in price paths are investigated to provide a risk analysis for firms that work in such market conditions. With the advent of the big data era, information about consumers and competitors gives firms a greater control over uncertainty than ever before. Simulations will demonstrate that firms can lower the volatility of their price path if they gather and process this information. Furthermore, the feedback forms of the optimal price path are derived in both the absence and the presence of both competition and reference-price effects. In general, the impact that demand uncertainty has over the firm’s pricing strategy is determined by a combination of the firm’s discount rate, demand uncertainty, and demand-side/cost-side dynamics.