Given sexual conflict, mating encounters between simultaneous hermaphrodites will conform to a new, conditional, non-zero sum game of strategy, the Hermaphrodite's Dilemma; special cases of which include Prisoner's Dilemma and Game of Chicken. The model predicts that hermaphrodite mating systems will be based on reciprocation with cheating in a preferred sexual role. This model suggests that study of hermaphrodite mating systems will provide direct evidence for the existence of sexual conflict and suggests that sexual conflict may act to stabilize hermaphroditism through such mating systems.