A two-person game is of conflicting interests if the strategy to which player one would most like to commit herself holds player two down to his minimax payoff. Suppose there is a positive prior probability that player one is a "commitment type" who will always play this strategy. Then player one will get at least her commitment payoff in any Nash equilibrium of the repeated game if her discount factor approaches one. This result is robust against further perturbations of the informational structure and in striking contrast to the message of the Folk Theorem for games with incomplete information.