Do Firms Maximize? Evidence from Professional Football
以美国国家橄榄球联盟中第四次进攻时的决策为例，检验竞争是否导致企业做出最大化选择。通过逐场数据和动态规划估计不同情境下的平均收益，发现实际决策系统性地偏离了最大化获胜概率的选择。
This paper examines a single, narrow decision—the choice on fourth down in the National Football League between kicking and trying for a first down—as a case study of the standard view that competition in the goods, capital, and labor markets leads firms to make maximizing choices. Play-by-play data and dynamic programming are used to estimate the average payoffs to kicking and trying for a first down under different circumstances. Examination of actual decisions shows systematic, clear-cut, and overwhelmingly statistically significant departures from the decisions that would maximize teams' chances of winning. Possible reasons for the departures are considered.