In 1944, the Allies were planning an operation for the liberation of Europe, and
ID: 1093047 • Letter: I
Question
In 1944, the Allies were planning an operation for the liberation of Europe, and the Nazis were playing their defense against it. There were two possibilities for the initial landing ? the Normandy beaches and pas de Calais. A landing would surely succeed against a week defense, so the Germans would have to concentrate their attention on one of these two places. Calais was more difficult to invade, but more valuable to win, being closer to the Allies? ultimate targets in France, Belgium, and Germany itself. Suppose the probabilities are success are as follows: Probabilities of Allied Success German defense Allied landing Normandy 75% 100% Calais 100% 20%Explanation / Answer
This question is a typical question of Game Theory.
To understand this we must first consider two assumptions:
1) both the allies and the germans are rational and both of them have knowledge of the results of the invasion.
2) The outcomes of the invasion are reasonable and correct and thus there shall not be any ex-post regret.
If these two conditions are satisfied then we believe that a Nash-Equlibrium shall exist and there shall be an optimal strategy to solve this problem.
let us construct the payoffs of the invasion as (Allies,Germans), N: Normandy, C: Calais
(N,N) = (0,0) probability of allied success = 75%
(N,C) = (80,-80) probability of allied success = 100%
(C,N) = (100,-100) probability of allied success = 100%
(C,C) = (0,0) probability of allied success = 20%
If the commander chooses C, he knows that the marshall will act rationally and will choose C instead of N, and the allied with 20% probability shall loose.
If the commander chooses N, he know that the marshall will act rationally and will choose N instead of C, and the allied with 75% probability shall win.
In totality the Marshall knows that the commander knows that he has higher probability of winning at if the invasion takes place at Normandy. So the marshall shall act rationally and defend at Normandy.
Thus the nash-equlibrium suggests that (N,N) is the best possible outcome