极小极大值理论的历史发展

A tentative discussion on the evolution of the minmax theorem

就博弈论早期史这一问题,采用考证原著的方法,针对极小极大值理论早期发展的历史进行了研究。认为:历史上第一个极小极大值解是法国数学家瓦德哥锐于1713年得到的,但在此后的两个世纪中,这一结果一直没有引起人们的注意。直到20世纪20年代,波莱尔在研究二人零和博弈时才重新得出了极小极大值解的概念,而极小极大值定理的正式提出和证明则是由冯·诺伊曼于1928年完成的。此后,这一定理的证明又进一步得到了简化和完善。

A study on literatures of early games theory indicated that the first minimax solution in history was found by Jame Waldegrave in 1713.But Waldegrave′s solution has almost been neglected for two centuries.It was E.Borle who found the minimax solution again in 1920s. And von Neumann gave the first proof of the minimax theorem for twoperson strategy games in 1928.The proof of the minimax has been improved and perfected from then.