When an individual or an organization makes a decision choice, if the selected object is also optional, it is called a two-way decision making behavior. In the context of two-way choice, how the two sides should conduct the optimal choice behavior is the subject of this research. Gale and Shapley (1962) proposed the Gale-Shapley algorithm (GS algorithm), which allows both-side decision makers to find the optimal pairing. Because the method has the characteristics of deferred acceptance, this study will use the GS algorithm to construct a two-way optimal selection strategy model, and prove that the active attacker has a first-mover advantage.