In game theory, it is assumed that each individual player is trying to maximize his own advantage by taking into account the strategy adopted by the other players. The application of game theory in general, and the prisoner's dilemma game in particular, is not unusual in the study of the Taiwan Strait relation. By building a mutual trust mechanism, it was concluded that a win-win solution can be found in the cross-strait prisoner's dilemma game. The Taiwan Strait conflict, however, stems from a long-standing disagreement between the two sides over the issue of independence versus unification. Each side keeps their basic position without compromise is not an unrealistic assumption. The optimum solution for the prisoner's dilemma game may then be overcome by the structure change of the game, leading to the possibility of a superior outcome. In this paper, we develop a game-theoretic model to study the conditions under which a game structure change can actually work to prevent both sides from provoking each other.