Minimax Play at Wimbledon: Comment
重新检验了Walker和Wooders（2001）关于网球发球策略的极小极大均衡假说，使用更广泛的数据集（包括男子、女子和青少年比赛），发现该假说得到更强支持，发球方向胜率相等且序列独立。
In a recent contribution, Mark Walker and John Wooders (2001) analyzed serve choices in Grand Slam tennis matches to provide an empirical test of the mixed strategy equilibrium. They argued convincingly that unlike subjects in laboratories, professional players have sufficient experience to play games well, and that they are also highly motivated to win these games. Their results indicated that there were no statistical differences in win rates for male players across various strategies, which is consistent with the equilibrium prediction. They fairly noted, however, that even the top male players tended to switch from one strategy to another too often, resulting in serial dependence. This paper reexamines the results of Walker and Wooders (2001) by collecting and analyzing a broader dataset, including men’s, women’s, and juniors’ matches. We find that the support of the minimax hypothesis is stronger. The plays in our data pass all of the tests in Walker and Wooders (2001) and therefore are more consistent with the theory of equilibrium than those in Walker and Wooders (2001). In short, the two hypotheses implied by the equilibrium, i.e., the equal probability of winning serve directions and the serial independence of serves, are borne out in our data.