Price and guaranteed delivery time competition/cooperation in a duopoly

In this paper, we explore the competition and cooperation in a duopoly setting where two facilities dominant control over a market. The demand faced by each facility is not only sensitive to its own retail price and guaranteed delivery time, but also to the differences between the two prices and guaranteed delivery times. We extend the works in the literature by considering competition and cooperation in duopoly. We analyze three different competition scenarios where the two facilities compete exclusively on retail prices, exclusively on guaranteed delivery times and both on retail prices and guaranteed delivery times, and three different cooperation scenarios where they cooperate exclusively on retail prices, exclusively on guaranteed delivery times, and both on retail prices and guaranteed delivery times. Research results reveal that the competition on retail prices for given guaranteed delivery times is as same as the Bertrand game, reaching to the Nash-Bertrand equilibrium, the equilibrium guaranteed delivery time of each facility for given retail prices only depends on its own retail price, and when price is a decision variable, the gross profits of the facilities increase significantly via coordinating retail prices.