Investigation of the Best Response Function for Hotel Revenue Management with Concurrent Bookings of Two Fare Classes

We consider a situation in which the booking requests from different fare classes arrive concurrently and two hotels compete with each other. Under this game theoretic setting, this problem was formulated as a two-player two-fare-class dynamic game. The main contributions can be presented as follows. First, each hotel\´s optimal future revenue is a non-decreasing function of its own room inventory and a non-increasing function of the other hotel\´s room inventory at any time. Secondly, we show that the non-increasing property of marginal profit well fits the classical "marginal revenue decreasing" law in economics. Finally, by using expected marginal value of hotels\´ room, we simplify the optimal accept/reject decision into sets of critical values.