Governments often seek influence beyond their borders. One way is through what Thomas Schelling (1960, 1966) calls brute force, taking direct physical control. Less extreme methods are to promise rewards for taking desired actions, or to threaten punishments for not carrying them out-sanctions. Sanctions involve two parties, the sender and the target. (To help identify pronouns' antecedents, we consider a feminine sender and masculine target.) The sender's objective is to influence the target by threatening to impose some measure against him for acting contrary to her interest. Sanctions have long been important in international relations. Athens imposed a trade embargo against Megara, ultimately setting off the Peloponnesian War (431-404 BC). Sanctions are central to such international agreements as the United Nations Charter, the World Trade Organization, and the Montreal Protocol governing chlorofluorocarbons. U.S. law prescribes the use of sanctions in circumstances related, for example, to national security, human rights, intellectual property, and international trade.' Do sanctions actually achieve senders' objectives? A common claim is that they usually fail and are costly to senders. Recent U.S. legislation proposes to limit unilateral U.S. sanctions (except trade-related ones), on the grounds that they cost more than they are worth. History provides examples of sanctions that were costly and ineffectual, such as the League of Nations sanctions against the Italian occupation of Abyssinia, or U.S. sanctions against Cuba. United Nations sanctions against Iraq remain in place, having achieved less than full success, to say the least (see Gary Hufbauer et al., 1990). More systematic studies suggest that sanctions often do succeed, particularly when objectives are modest. Hufbauer et al. (1990) examine 116 episodes of sanctions with military or political objectives, deeming about one-third successful. Sanctions imposed under U.S. trade law have worked even better, about three-fourths of the time (see e.g., Sykes, 1992; Thomas Bayard and Kimberly A. Elliott, 1994; Elliott and J. David Richardson, 1997). Here we develop a simple framework to explain how sanctions can worl, and what is required for them to succeed. Our framework exploits advances in the theory of repeated games and bargaining under incomplete information. While a game-theorist would recognize the flavor of our results, the setting here is a fresh one.2 We find success more likely when the threatened measure costs the sender little relative to the gain from modifying the target's behavior, while the damage to the target is large relative to his cost of complying with the sender's will-results consistent with both intuition and empirical evidence (as well as with Adam Smith [1776 Book IV, Ch. I]). Moreover, a more patient sender is more likely to succeed, while the target's patience can work to the sender's disadvantage.3
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