When to Appease and When to Punish: Hitler, Putin, and Hamas

David K. Levine& Lee E. Ohanian in this paper discuss when to appease and 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.

Findings:

We report two main findings that provide a deeper and more nuanced understanding of the process of punishment and appeasement, and how these choices relate to understanding strong and weak incumbents. Absent the need to signal intentions, we find there is a pooling equilibrium in which it is always better to appease the challenger in the sense of delaying punishment for the first stage until after the second stage. In the pooling equilibrium, appeasement is a signal of strength, thus turning on its head the conventional view that appeasing an invader is a sign of weakness that invites subsequent attacks.

We also find conditions under which equilibrium appeasement does reveal a weak incumbent,and thus provides new insights about the standard view of appeasement. Depending on the costs of the trade-offs involved in punishing, there can be an optimal separating equilibrium with signaling in which the strong type punishes at the end of the first stage, thus signaling strength, and in which the challenger does not launch a primary attack. In contrast, the weak type revokes their commitment to attack in this equilibrium. The weak type appeases the probative attack, and thus suffers a primary attack in the second stage as the challenger correctly expects they will not be punished if they launch a primary attack.