Game theory and diplomatic history: The strategy behind the Rhineland crisis
Now that you’ve been armed with the basics of Game Theory and the background to the Rhineland Crisis of 1936, we can go about analysing it. In the final part of our series on Game Theory, Frank Zagare uses the theory to analyse the thinking behind the actions of France and Germany as German Military Forces violated the terms of the Treaty of Versailles by entering the Rhineland. This adapted excerpt comes from Game Theory, Diplomatic History and Security Studies.
Notice that, in March 1936, neither Germany nor France preferred to act on their (deterrent) threats. If the French resisted, German decision makers preferred to back down, while French leaders were similarly intent on avoiding the costs of another all-out war. In other words, given their preferences, neither player’s threat to resist was credible to execute (or rational to carry out). Players with an irrational (or incredible) threat can be called as Soft, and by contrast, a player with a credible threat called Hard. Clearly, in 1936, both Germany and France were Soft. Of course, both players knew their own type, that is, whether they were Hard or Soft. But neither knew the other’s type (preferences). Had they had this information, the status quo would have held, deterrence would have succeeded, and there would have been no crisis. Given complete information about German preferences, the French would have rationally stood firm (at Node 2), forcing the Germans to (rationally) back down (at Node 3). Knowing this, Hitler would have (again, rationally) postponed the remilitarization in order to avoid humiliation and, perhaps, as he feared, removal from office.
All of which is to say that the crisis of 1936 was a game of incomplete information — at least one player does not know another’s preference function.
In a strategic form game with incomplete information, the accepted standard of rational play is called a Bayesian (Nash) equilibrium, which is defined as a strategy combination that maximizes each player’s expected utility, given that player’s (subjective) beliefs about the other players’ types. The natural extension of this concept to a dynamic game, such as this one, is called a perfect Bayesian equilibrium.
A perfect Bayesian equilibrium specifies an action choice for every type (in this example, Hard and Soft) of every player at every decision node (or information set) belonging to the player; it must also indicate how each player updates its beliefs about other players’ types in the light of new information obtained as the game is played out. As it turns out there are five perfect Bayesian equilibria in the Unilateral Deterrence Game, but only one that is both plausible and consistent with the preferences and the beliefs of German and French decision makers in 1936. Hence, an explanation is (almost) at hand.
For reasons that will shortly become obvious, this equilibrium is called Attack. Under the Attack Equilibrium, a Challenger (i.e., Germany) demands an alteration of the Status Quo (at Node 1), regardless of its type, but a Soft Challenger (which Germany was in 1936) plans to back down (at Node 3) in the event that the Defender (i.e., France) resists at Node 2. For their part, Hard Defenders always resist at Node 2, and Soft Defenders (like France in 1936) always concede.
The explanation that is derived from this combined with both the beliefs and the action choices of the players during the Rhineland crisis is unexceptional and conforms with standard explanations of the event: in 1936, Hitler was a risk taker who was bluffing; his gamble that the French would accept a rollback of the status quo paid off handsomely.
But this unexceptional explanation should not obscure the point of the exercise: to illustrate in the simplest possible way how game models provide causal explanations.
Game-theoretic models map out the behavioral implications of various combinations of player preferences and, in the case of a game of incomplete information, beliefs. These implications specify the action choices that define an equilibrium and which, given the rationality assumption, should be observed when the game is actually played out. An explanation is achieved whenever predicted behavior and observed behavior are the same.
Fancy analysing another fascinating event in military history using Game Theory? Learn about how it can be used to analyse the Moroccan crisis of 1905–6, the first in a series of early twentieth-century confrontations generally considered to have led to World War I, with this free chapter.
Frank C. Zagare is UB Distinguished Professor of Political Science at the University at Buffalo, The State University of New York (SUNY). Professor Zagare’s main research interests lie in the nexus between security studies and game theory. He is the author of Game Theory, Diplomatic History and Security Studies (OUP, 2018).
