Collaborative Research: The Nonatomic-Game Approach to Revenue Management Under Competition

提案摘要？合作研究：竞争条件下收益管理的非原子博弈方法？该补助金提供资金的收入管理问题的非原子博弈均衡的表征。 由于其固有的困难，在竞争环境中的收入管理问题还没有得到充分的研究。 这个项目将避免多公司互动所带来的复杂性，通过无限公司的极端，考虑一个连续的公司，其中没有任何明显的影响，对市场的整体演变。 该项目的重点将是建立和描述相互支持的均衡市场过程和定价政策。 两种类型的问题，涉及随机和价格敏感的需求到达将被处理，每一个构成其独特的挑战。 在一种类型中，公司可以从一系列价格中自由选择，而在另一种类型中，公司不能重新审视它们自己收取的价格。 将研究确定性对应物，作为大容量限值的基准，并进行计算研究，以评估无限公司近似值的适当性。 如果成功的话，本研究的结果将导致更深入地了解竞争性收入管理问题。 本研究的一般方法、具体工具和中间结果可能适用于其他地方的理论研究。 特别是，Knaster-Taski和Kakutani-Glicksberg-Fan不动点定理的新用途可能会激发进一步的研究。 平衡定价政策确定的项目将作为有用的指导方针，真实的公司实行动态价格调整，以应对竞争对手？价格变动。 拟议的计算研究将解决如何准确的无限坚定的近似的真实的有限坚定的设置可以的问题。 研究结果将被证明是更切实可行的，如果事实证明，更少的公司需要，以实现强大的激励真实的公司采用非原子博弈定价均衡。

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.