This article employs game theory to analyze two games played at the Paris Peace Talks of 1968-1973 by the United States, the Republic of Vietnam, and a coalition of the Democratic Republic of Vietnam and the National Liberation Front. The stalemate of the first game, which lasted from the inception of the Talks in 1968 to the winter of 1971-1972, is shown to have resulted from the coincidence of the preferences of the players and from their game-theoretically defined best strategies. The article offers two interpretations of the outcome of the second game. Under the first interpretation, the two-track solution, the most-preferred alternative of the United States, is shown to have resulted from a shift in the Commumsts' preference order. Under the second, this game is shown to be vulnerable to a deceptive strategy by the United States. Under either interpretation, the optimal strategy of the United States entailed announcing that it would prefer to prolong the war rather than capitulate to the Communists.