Despite repeated U.S. claims that its policy toward relations across the Taiwan Strait is ?consistent? and ?clear,? in actuality its policy has long been one of ?strategic ambiguity.? It is widely recognized by scholars and policy-makers alike that the so-called Taiwan question is the most potentially explosive issue in U.S.-P.R.C relations.What is the strategic ambiguity policy all about? What role has it played in influencing the equilibrium outcomes of cross-Strait relations in the past three decades? How are the dynamics of the ?strategic triangle? consisting of the United States, Mainland China and Taiwan to be understood? How effective in preserving peace across the Taiwan Strait is U.S. policy of strategic ambiguity likely to be in the future? Few studies, if any, have provided theoretical answers to these questions. This paper tries to develop a game theoretic model which may provide tentative answers to these interesting, unresolved questions. Supporters of the ?strategic ambiguity? policy argue that it has successfully kept the Strait free of conflict: on the one hand, Mainland China always has to take into account the possibility that the United States might intervene if it were to attack Taiwan, and on the other hand, Taiwan always has to think twice before ?going too far? (such as declaring formal independence from the mainland). The policy, it is said, has served U.S. national security interests and has effectively accommodated changes in cross-Strait relations in past decades. There are opposing opinions, however. The dissolution of the Soviet Union and the end of the Cold War have rendered one of the major imperatives for a U.S.-China rapprochement and compromises on Taiwan?the basis of the strategic ambiguity policy?obsolete. Moreover, the democratization of Taiwan and the increasing military threat if faces, such as the deployment of missiles by Mainland China aimed at Taiwan, have brought new variables into the equation. Taiwan?s thriving democracy has added ideological values and moral imperatives to the U.S. commitment of defending the island. The increasing military threat from Mainland China, meanwhile, seems to have strengthened the argument for an increasing commitment to Taiwan?s defense, either in the form of more military sales or coordination between U.S. and Taiwan militaries. A continuing ambiguity in U.S. policy, so the arguments goes, will encourage PRC militancy and frustrate Taiwan?s determination to resisting aggression, and may be prone to disrupt the delicate equilibrium. Above all, it seems to compromise the U.S. moral imperative of defending democratic values.Our model shows that the policy of strategic ambiguity helps preserve the status quo and maintain peace and stability across the Taiwan Strait. The strategic ambiguity policy is a defensive strategy in nature, well-suited at deterring both Mainland China and Taiwan from deviating from equilibrium strategies. In the long run, the strategic ambiguity policy, however, needs to be supplemented, if not replaced, by more imaginative policies in order to successfully manage the Taiwan issue. For example, the United States could be more forthright in proposals that help to eliminate potential conflicts of interest, such as proposing that Mainland China renounce the use of force to resolve the Taiwan issue in exchange for Taiwan?s pledge not to pursue independence. ..PAT.-Conference Proceeding [ABSTRACT FROM AUTHOR]