Professionals Play Minimax
利用职业足球比赛罚点球的自然数据，检验了极小极大定理的均衡预测，发现球员的选择在获胜概率和序列独立性上均与均衡一致，首次在自然条件下支持该定理的两个推论。
The implications of the Minimax theorem are tested using natural data. The tests use a unique data set from penalty kicks in professional soccer games. In this natural setting experts play a one-shot two-person zero-sum game. The results of the tests are remarkably consistent with equilibrium play in every respect: (i) winning probabilities are statistically identical across strategies for players; (ii) players' choices are serially independent. The tests have substantial power to distinguish equilibrium play from disequilibrium alternatives. These results represent the first time that both implications of von Neumann's Minimax theorem are supported under natural conditions. Copyright 2003, Wiley-Blackwell.