Both France and Taiwan's political systems are semi-presidential. However, ”cohabitation” in French constitutional experience has occurred three times while Taiwan has never seen ”cohabitation” until now. Finding the reason for this difference is the central question of this paper. By using the game theory as an analysis tool, the paper explores how the institutional design influences the actors' strategic interactions, which underlies the discrepancy between France and Taiwan in ”cohabitation”. France and Taiwan have different electoral systems and different safeguard clauses of the congressional term. Therefore, differences in political calculations and strategic interactions are the two institutional factors that result in the president and the parliamentary majority belonging to different party coalitions, and which lead to the fact that France has seen ”cohabitation” while Taiwan has not.