A Nonatomic-Game Approach to Dynamic Pricing under Competition

We study a revenue management problem involving competing firms. We assume the presence of a continuum of infinitesimal firms where no individual firm has any discernable influence over the evolution of the overall market condition. Under this nonatomic-game approach, the unanimous adoption of an equilibrium pricing policy by all firms will yield a market-condition process that in turn will elicit the said policy as one of the best individual responses. For both deterministic- and stochastic-demand cases, we show the existence of equilibrium pricing policies that exhibit well-behaving monotone trends. Our computational study reveals many useful insights, including the fact that only a reasonable number of firms are needed for our approach to produce near-rational pricing policies.