This article proposes a tool for describing historical changes as interactions between influential leaders' choices and public sentiment. For this purpose, I first point out another type of micro-macro linkage for social change that complements the type of micro-macro link described by Coleman's boat. Second, I propose an “initial condition game” of Richardson's arms race model as a concrete example of the above framework. The initial condition game represents an interdependent rational choice situation for influential players on the premise of public sentiment. In terms of the mathematical analysis of arms race and armed conflict, the initial condition game can be regarded as an attempt to integrate deterministic differential equation models with the strategic game theoretic models of arms races. Several cases of the initial condition game are analyzed as exemplars.