Negotiation statements with promise and threat

A negotiator, in order to achieve her goal, must induce an agent to cooperate. The agent faces costs or risks for cooperating. I develop a game-theoretic model where the negotiator may issue a negotiation statement that contains a threat of punishment for non-cooperation and a promise of reward for cooperation; after which the agent must choose either to cooperate or not. I derive necessary and sufficient conditions under which combining a threat with a promise is effective and credible in inducing the agent’s full cooperation. I discuss insights from the model in the context of two applications. My analysis provides a rationale for the use of both promise and threat in negotiations to establish cooperation, increasing the chance of achieving the negotiator’s goal.