The Genesis of Differential Games in Light of Isaacs? Contributions

Abstract

Rufus P. Isaacs joined the RAND Corporation4, Santa Monica, California in 1948 and started to develop the theory of dynamic games in the early 1950s. Until winter 1954/55, when Isaacs left the RAND Corporation, he investigated two player, zero-sum dynamic games of the classic pursuit-evasion type. Prior to 1965, Isaacs published his theory only in internal RAND papers and research memoranda. In his first RAND paper (Ref. 1), Isaacs sketched the basic ideas of zero-sum dynamic game theory. The ideas already included rudimentary precursors of the maximum principle, dynamic programming, and backward analysis. At the end of 1954 and the beginning of 1955, Isaacs summarized his research in four research memoranda (Refs. 3--6), which ten years later formed the basis of his famous book on Differential Games (Ref. 7). This paper surveys Isaacs’ research with an emphasis on the early years of dynamic games. The readers are kindly invited to discuss the author’s point of view. Comments and statements sent to the author will be summarized and published later.