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

建议摘要“合作研究：竞争下收入管理的非原子博弈方法？”这项拨款为描述收入管理问题的非原子博弈均衡提供了资金。由于其固有的困难，在竞争环境下的收入管理问题没有得到充分的审查。这个项目将通过走向无限公司的极端来避免多公司相互作用带来的复杂性，考虑到其中没有一家公司对市场的整体演变产生任何明显影响的公司的连续体。该项目的重点将是建立和描述相互支持的均衡市场程序和定价政策。涉及随机和对价格敏感的需求到达的两类问题将被解决，每一类问题都构成了独特的挑战。在一种类型中，公司可以从价格菜单中自由选择，而在另一种类型中，公司不能重新审查他们自己收取的价格。确定性的对应物将被作为大容量限制的基准进行研究，并将进行计算研究，以评估无限公司近似的适当性。如果研究成功，本研究的结果将有助于对竞争性收益管理问题的更深入的理解。这项研究的一般方法、具体工具和中间结果很可能适用于其他地方的理论努力。特别是，Knaster-TASki和Kakutani-Glicksberg-Fan不动点定理的新颖应用可能会启发进一步的研究。该项目确定的均衡定价政策将作为实际公司实施动态价格调整以应对竞争对手的有用指导？价格走势。拟议的计算研究将解决这样一个问题，即无限公司对真实的有限公司设置的近似可以有多准确。如果事实证明，为了实现对真实企业采用非原子博弈定价均衡的强烈激励，需要更少的企业，那么研究结果将被证明是更可行的。

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.