Computing pure Nash equilibria in network revenue management games

We present a mixed-integer model to optimize a competitor’s behavior in a network revenue management game. Our model is based on a well-known deterministic linear program for the single-airline network revenue management problem. Assuming that the competitors make decisions based on our model, we present an algorithm to compute a pure Nash equilibrium (NE) in a two-player game through an iterative search for best responses. If the algorithm gets stuck in a loop without finding an NE, additional constraints are added to the models to control the search. The complete algorithm finds an NE with certainty if one exists in the game. The players’ price vectors are modified so that their models have unique solutions, and the search follows a unique path. This makes sure that both players end up in the same NE even if uniqueness is not guaranteed or cannot be proved. A computational study shows the algorithm’s performance which can compute NE in networks of realistic size in acceptable time.