Subgame perfect Nash equilibrium for dynamic pricing competition with finite planning horizon

TL;DR

This paper analyzes the subgame perfect Nash equilibrium in dynamic pricing competition among firms with fixed capacities and stochastic demand over a finite horizon, revealing unique equilibrium strategies in duopoly and oligopoly settings.

Contribution

It introduces a stochastic dynamic programming approach to characterize equilibrium prices in finite-horizon, competitive markets with perishable goods and demand uncertainty.

Findings

Duopoly has a unique Nash equilibrium under binary demand.

Oligopoly does not show price dispersion with binary demand.

Generalized demand leads to unique mixed strategy equilibria in both duopoly and oligopoly.

Abstract

Having fixed capacities, homogeneous products and price sensitive customer purchase decision are primary distinguishing characteristics of numerous revenue management systems. Even with two or three rivals, competition is still highly fierce. This paper studies sub-game perfect Nash equilibrium of a price competition in an oligopoly market with perishable assets. Sellers each has one unit of a good that cannot be replenished, and they compete in setting prices to sell their good over a finite sales horizon. Each period, buyers desire one unit of the good and the number of buyers coming to the market in each period is random. All sellers' prices are accessible for buyers, and search is costless. Using stochastic dynamic programming methods, the best response of sellers can be obtained from a one-shot price competition game regarding remained periods and the current-time demand structure. Assuming a binary demand model, we demonstrate that the duopoly model has a unique Nash equilibrium and the oligopoly model does not reveal price dispersion with respect to a particular metric. We illustrate that, when considering a generalized demand model, the duopoly model has a unique mixed strategy Nash equilibrium while the oligopoly model has a unique symmetric mixed strategy Nash equilibrium.