Dynamic Pricing of Perishable Assets Under Competition

Existing revenue management solutions employed by legacy carriers, which are based on allocating capacity to pre-defined fare classes, are increasingly inadequate to compete against low-cost carriers that impose few or no fare restrictions and make their fares widely available through the Internet. To avoid revenue erosion due to inadequate solutions, legacy carriers need to develop systems that take into account consumer purchasing behavior which itself depends on the fares available at the time of purchase. This requires a choice-based, multi-player, game theoretic formulation of dynamically pricing perishable capacities over finite horizons. Here we present such a formulation as a stochastic game in continuous time. Since this problem is generally intractable, we provide sufficient conditions for the existence of open-loop and closed-loop Nash equilibria of the corresponding differential game resulting from an affine functional approximation approach to the stochastic problem. We show that efficiently-computable pricing heuristics based on these open-loop and closed-loop policies are asymptotic equilibria in an appropriate sense for the stochastic game under various information assumptions.