When to Appease and When to Punish

Much has been written about deterrence, the process of committing to punish an adversary to prevent an attack. But in sufficiently rich environments where attacks evolve over time, formulating a strategy involves not only deterrence but also appeasement, the less costly process of not responding to an attack. This paper develops a model that integrates these two processes to analyze the equilibrium time paths of attacks, punishment, and appeasement. We study an environment in which a small attack is launched and can be followed by a larger attack. There are pooling and separating equilibria. The pooling equilibrium turns the common intuition that appeasement is a sign of weakness, inviting subsequent attacks, on its head, because appeasement is a sign of strength in the pooling case. In contrast, the separating equilibrium captures the common intuition that appeasement is a sign of weakness, but only because deterrence in this equilibrium fails. We interpret several episodes of aggression, appeasement, and deterrence: Neville Chamberlain's responses to Hitler, Putin's invasion of Ukraine, Israel's response to Hamas, Turkey's invasion of Cyprus, and Serbia's attacks in Kosovo.

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