Threats Without Binding Commitment

This paper explores the power of threats in the absence of binding commitment. The threatener cannot commit to carry out the threat if the victim refuses payment, and cannot commit not to carry out the threat if payment is made. An important assumption of the model is that once the threat is carried out it cannot be repeated. If exercising the threat is costly to the threatener, then the threat cannot succeed in extracting money from the victim. If exercising the threat would benefit the threatener, however, then the threat's success depends upon whether the threat may be repeated after a payment is made. In the equilibrium of a finite-period game, the threat is carried out and the victim makes no payments. In an infinite-horizon game, however, it is an equilibrium for the victim to make a stream of payments over time. The expectation of future payments keeps the threatener from exercising the threat.