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

• Published in: IDEAS Working Paper Series from RePEc
• Main Author: Fadavi, Niloofar
• Format: Paper
• Language: English
• Published: St. Louis Federal Reserve Bank of St. Louis 01.01.2022
• Subjects: Competition; Duopoly; Equilibrium; Game theory

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.