Abstract of Proposal "Collaborative Research: The Nonatomic-Game Approach to Revenue Management under Competition?
The grant provides funding for the characterization of nonatomic-game equilibria of revenue management problems. Due to its innate difficulty, revenue management problems in competitive settings have not been adequately examined. This project will avoid complexities posed by multi-firm interactions by going to the infinite-firm extreme, considering a continuum of firms among whom none has any discernible impact on the overall evolution of the market. The focus of the project will be the establishment and characterization of equilibrium market processes and pricing policies that mutually sustain one another. Two types of problems involving stochastic and price-sensitive demand arrivals will be tackled, with each posing its unique challenges. In one type, firms can freely choose from a menu of prices, while in another type, firms cannot revisit prices they have themselves charged. Deterministic counterparts will be studied as benchmarks for heavy-volume limits, and computational studies will be conducted to assess the appropriateness of the infinite-firm approximation. If successful, results of this research will lead to a deeper understanding of competitive revenue management problems. General methods, specific tools, and intermediate results of this research will likely be applicable to theoretical endeavors elsewhere. In particular, novel uses of the Knaster-Taski and Kakutani-Glicksberg-Fan fixed point theorems may inspire further research. Equilibrium pricing policies identified by the project will serve as useful guidelines to real firms practicing dynamic price adjustments in response to competitors? price movements. The proposed computational study will address the problem of how accurate the infinite-firm approximation of the real finite-firm setting can be. Research outcomes will prove to be more practicable if it turns out that fewer firms are needed in order to realize strong incentives for real firms to adopt nonatomic-game pricing equilibria.
