A Mean Field Competition

• 成果类型: Article
• 署名作者: Nutz, Marcel; Zhang, Yuchong
• 署名单位: Columbia University; Columbia University; University of Toronto
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0966
• 发表日期: 2019
• 页码: 1245-1263
• 关键词: finite-state; games; contests; systems; extension; PLAYER; RISK

摘要

We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and are paid a reward based on their relative rank. First, we propose a tractable Poissonian model in which we can describe the optimal effort for a given reward scheme. Second, we study the principal-agent problem of designing an optimal reward scheme. A surprising, explicit design is found to minimize the time until a given fraction of the population has reached the goal.