Pricing in revenue management for multiple firms competing for customers

We consider the pricing strategies of multiple firms providing the same service in competition for a common pool of customers in a revenue management context. The firms have finite capacity and the demand at each firm depends on the selling prices charged by all firms, each of which satisfies demand up to a given capacity limit. We use game theory to analyze the systems when firms face either a deterministic demand or a general stochastic demand. The existence and uniqueness conditions of a Nash equilibrium are derived, and we calculate the explicit Nash equilibrium point when the demand at each firm is a linear function of price. We also conduct sensitivity analysis of the equilibrium prices with respect to cost and capacity parameters.