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

“合作研究：竞争下收益管理的非原子博弈方法？”该赠款为收入管理问题的非原子博弈均衡的表征提供资金。由于其固有的困难，竞争环境下的收入管理问题没有得到充分的审查。这个项目将避免多公司相互作用所带来的复杂性，通过走向无限公司的极端，考虑到一个连续的公司，其中没有一个对市场的整体演变有任何明显的影响。该项目的重点将是建立和确定相互维持的均衡市场过程和定价政策的特征。涉及随机需求和价格敏感需求的两类问题将得到解决，每种问题都有其独特的挑战。在一种类型中，企业可以从价格菜单中自由选择，而在另一种类型中，企业不能重新调整自己设定的价格。确定性对应物将作为大体积限制的基准进行研究，并且将进行计算研究以评估无限公司近似的适当性。如果成功，本研究的结果将导致对竞争性收入管理问题的更深层次的理解。本研究的一般方法、特定工具和中间结果可能适用于其他地方的理论努力。特别是，Knaster-Taski和Kakutani-Glicksberg-Fan不动点定理的新应用可能会激发进一步的研究。该项目确定的均衡定价政策将为实际企业在应对竞争对手时进行动态价格调整提供有用的指导。价格变动。提出的计算研究将解决实际有限公司设置的无限公司近似的精确度问题。如果需要更少的企业来实现对真实企业采用非原子博弈定价均衡的强激励，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.