A game theory essay examining the story behind a city's sacrifice.
On the night of November 14, 1940, 449 bombers from the German air force, known as the Luftwaffe, filled the skies above the city of Coventry, England. The horror that was to follow marked one of the most brutal attacks on civilians in the history of the world. 56 tons of incendiaries, 394 tons of high explosives, and 127 land mines rained down upon the city, killing 550 people, destroying 50,000 homes, and perhaps most notably of all, obliterating the fourteenth-century St. Michaels cathedral. Maybe the most unsettling aspect of this massacre, however, is the notion that it was preventable—that Prime Minister Winston Churchill knew about it days in advance, but took no countermeasures to halt the carnage. What would prompt someone to knowingly leave a city and its inhabitants to be slaughtered? As it turns out, this account of the story behind the destruction of Coventry is a myth—Churchill didn’t know that the Germans had their sights set on Coventry until it was too late. Myth or not, however, the story behind this fateful night offers many insights into how Churchill could have made such a drastic choice. This paper will give an overview of the tale behind this horrible incident, and then analyze, from a logical and game theoretical perspective, why his decision would have been the correct one.
The Nazis encrypted their wireless communications using a machine called Enigma. Before this, enciphering was done manually, which was a slow and laborious process, but Enigma could produce a nearly infinite number of different cipher alphabets simply and efficiently. The Germans believed that the Enigma code was unbreakable, for new keys were used each day, meaning that the chances of decryption seemed to be virtually non-existent. Meanwhile, however, some of the most brilliant minds in England—scientists, mathematicians, and cryptanalysts—had been toiling in a Victorian mansion at a location called Bletchley Park, also known as Station X, to create a device that would intercept and decode German messages. This secret project was code-named Ultra, and in August 1939, the month before Hitler invaded Poland and embroiled the globe in World War II, Ultra cracked the Enigma code. The exact method by which this was achieved would be far too complicated to discuss here, but essentially, “The Bomb,” as it was called, matched the electrical circuits of Enigma and mimicked the daily change in its keying procedure, allowing the British (and later, the Americans) full access to the messages it sent (Breuer 44).
The Allies had to exploit this information with the utmost care, however. If the Germans sent messages detailing the exact time and location for their attacks, and the Allies were consistently prepared for their arrival, then the Germans would very quickly begin to suspect that Enigma had been broken, at which point they would develop a new cipher system, and all the effort and resources invested in Ultra would have been for virtually nothing. Because of this, the Allies could only capitalize upon secrets gleaned from The Bomb when they could devise a credible cover story to explain their knowledge, such as that the information was gathered from certain espionage activities (Lawson 10).
Was it Churchill’s desire to keep The Bomb a secret that led him to sacrifice Coventry? Donald Lawson (11) answers that question affirmatively, as does F.W Winterbotham, who was a link between the Secret Intelligence Service and the decrypters at Bletchley Park. Although most cities destined for bombing raids were given code names, “At about 3 PM on November the fourteenth, someone must have made a slip-up and instead of a city with a code name, Coventry was spelt out.” Winterbotham contends that he informed Churchill’s personal secretary of this development, since Churchill was at a meeting. If this account is true and Churchill did indeed know that Coventry was the doomed city well before the attack, Winterbotham does not find the Prime Minister at fault. “This is the sort of terrible decision that sometimes has to be made on the highest levels in war. It was unquestionably the right one, but I am glad it was not I who had to take it” (Winterbotham 60-61).
Despite these and several other claims that Churchill intentionally abandoned Coventry in its darkest hour, the vast majority of sources assert that this story is a complete fabrication. The legend seems to have arisen as a convenient refuge for those who preferred to believe that Coventry was destroyed as the result of a noble sacrifice instead of accepting the truth….
An Enigma decrypt from November 11 concerned a German operation called Moonlight Sonata. The name indicated that it was to be executed starting on the night of the next full moon, and that there were to be three phases. The targets were code-named Einheitspreis, Regenschirm, and Korn, which respectively translate to Unit Price, Umbrella, and Corn. Somehow, “unit price” was figured to mean “sixpence at Woolworth’s,” which was deduced to identify the city of Wolverhampton, partly due to the fact that a raid on Wolverhampton had been predicted. As it turned out, however, Wolverhampton was never attacked. “Umbrella” referred to former Prime Minister Neville Chamberlain, who was known for carrying an umbrella, and whose hometown was Birmingham (Lewin 101). The significance of “Korn,” on the other hand, eluded the British. As Robert Goldston (75) suggests, there is an area in London known as Cornhill, which might be one reason the British surmised that Korn represented the English capital. Churchill cancelled plans for a trip on the 14th because “he was not going to spend a peaceful evening in the country while the metropolis was under heavy attack.” As he stood on the roof of the Air Ministry building, gazing towards the horizon of the night sky and waiting for the German bombers to appear, the Luftwaffe launched its attack upon Coventry, the mysterious Korn, 100 miles away (Budiansky 182).
Winterbotham was correct that Coventry had been identified as the German target by 3:00 PM on November 14; however, this information did not come from Ultra. During the summer of 1940, the British Royal Air Force (RAF) had learned that the Germans were employing a new navigational aid to guide bombers to their targets, and to assist the pilots, many of whom were inexperienced at this point in the war, in flying at night. This apparatus was known as Knickebein, and later that summer, the Germans introduced two improved systems, X-Gerät and Y-Gerät. If the British could learn how to detect the path of the navigational beams and deflect them inconspicuously, then German bombs would fall on empty fields (West 12).
At 1:00 PM, the Germans began test transmissions of their navigational beams, and by 3:00, the RAF determined that Coventry was the target. The set of countermeasures enacted to thwart the Germans’ assault on Coventry was code-named Cold Water. In addition to intercepting and jamming the German navigational beams, Cold Water called for a counterattack on 27 Luftwaffe airfields in continental Europe and the eradication of the X-Gerät transmitter in Cherbourg, France. The British accomplished the latter two objectives, losing ten bombers in the process; however, they failed to jam the beams. The intended target of the raid was actually unimportant in relation to the countermeasures, for the RAF only had to know the frequency of the German signals to obstruct them and direct the bombers to where they would inflict little to no damage. Expecting this to occur, Churchill had absolutely no reason to order the evacuation and defense of Coventry. As it turns out, though, the RAF received the incorrect frequency, and the jammers had no effect. Although Cold Water resulted in the elimination of some German airfields and an X-Gerät transmitter, this error in frequency allowed the bombers to find their way to Coventry unhindered and dispense their deadly payload. The city was not condemned in order to protect the Ultra secret, but because of a severe mistake in intelligence or communication. This reality makes the story of Coventry’s fate seem much less grand and heroic, which could certainly help to explain why people were so willing to perpetuate the myth (West 16).
Although the popular story behind Coventry’s assault is a myth, and Churchill never had to decide whether or not to evacuate and defend the city, the following analysis will examine the hypothetical situation in which this was the case, and why he would have made his alleged choice. The fictional nature of this example does not render it trivial, for the same logic used here can be applied to many other situations. The final result of the investigation will seem obvious, and could have easily been arrived at through intuition—indeed, that’s probably what Churchill would have done—but this provides a slightly more formal view of the strategy involved. In each specific game, the payoffs will appear inside the terminal nodes, and the rollback equilibrium will be highlighted in yellow, but here is the basic setup:
Using the term “game” to refer to a battle—even a hypothetical one—in which human life will be lost probably appears amazingly callous if one doesn’t first understand that it’s the proper term in game theory to describe any strategic interaction, connoting nothing about the situation’s triviality or gravity.
Britain has the first move, and can choose to “Defend” Coventry (which includes civilian evacuation) or “Desert” Coventry, not offering any forewarning or assistance to the city’s authorities. Germany has the second move, and can choose to “Attack” Coventry or “Refrain” from attacking Coventry. In most of the games, not all decisions will be open to all players due to information asymmetry. In the end, who has more information proves to be the deciding factor in the overall outcome.
The following table illustrates the payoffs for different events that could occur. They are not mutually exclusive; that is, more than one can apply for each set of strategies between Britain and Germany.
The exact numbers are more or less arbitrary, for there is no way to quantitatively measure the effects of an attack, especially when placing a value on human life. Even if that were possible, however, calculating future payoffs as a result of these present actions would become horribly complex. If one didn’t assign payoffs to each of these events, instead choosing to rank each combination of Defend/Desert and Attack/Refrain based on relative preference, the same decisions would be made. The primary advantage of using these more specific payoffs is that it shows in a much clearer fashion who “wins” and who “loses,” and by how much.
Britain must expend a small amount of resources to evacuate Coventry and defend it, regardless of what the Germans do, which is why there is a small negative payoff associated with that event. If Germany attacks a defended city, then the British will be prepared with RAF fighter jets and/or anti-aircraft artillery, and Germany will suffer a loss. However, if Germany attacks an undefended city, then Britain will bear the loss, and a much greater one at that.
The next three events involve Enigma. If Germany knows Britain has decrypted Enigma, then Germany will develop a different system, and Britain loses a major advantage for the future. However, if Britain keeps the fact that it has decrypted Enigma a secret, then they will retain that advantage and have the option to use it against Germany in the future. If Germany somehow discovered that Enigma had been decrypted without Britain’s knowledge, however, then Germany could adopt a new system for true communications and use Enigma to send messages supplying Britain with false information, which could have severe consequences.
Before observing how the game would proceed considering Britain’s decryption of Enigma, it is important to note the outcome that would arise if Enigma were not involved at all.
If Britain had not decrypted Enigma, they would theoretically have no knowledge of the impending attack, so the Defend strategy would be unavailable, which is what the dashed lines reflect. Knowing that Britain will not defend Coventry, the superior payoff to Germany comes from attacking. Germany will obtain a payoff of 50 from attacking an undefended city, and Britain will receive the direct opposite.
Next, we examine the game from Coventry’s perspective. The payoff scheme is exactly the same as in the previous case. Although Britain has decrypted Enigma in this instance, this game is just about Coventry, so the future is not an issue.
Since Britain has decrypted Enigma, they know that Germany will attack. In light of this information, Britain will receive a payoff of 20 if they defend or –50 if they desert, so it is clearly in Britain’s best interest to defend Coventry. If people were faced with the same choice as Churchill, this would be many people’s instinctual reaction: When the government knows that an attack is imminent, they have a moral obligation to protect their citizens. Actually, as the following games indicate, that is precisely what the government is doing, except that obligation is better achieved through the opposite action.
The following game assumes the same information as the last: Britain has decrypted Enigma, and Germany is unaware of that; therefore, they will attack. However, after factoring in the effect of the Enigma machine on the future, the payoffs change significantly.
If Germany launched an attack on Coventry, only to find that the British had rolled out the red carpet and prepared for their arrival, the Germans would suspect that the secrecy of Enigma had been compromised, and the British would lose their advantage in the future. The British payoff for (Defend, Attack) is 100 less than in the previous game, and the German payoff is 100 greater. On the other hand, if Germany refrained from attacking, or if they raided a defenseless city, they would have no reason to believe that Britain had broken the Enigma code. This would raise Britain’s payoff by 200, and equally reduce Germany’s, in the remaining three outcomes. Thus, Britain’s payoff would be –80 for defending Coventry and 150 for deserting it, so Britain’s optimal choice is to desert. If one were to rank each country’s payoffs, Britain is receiving their second worst, while Germany is receiving their second best, but Britain is the clear victor. This demonstrates how using more assessable payoffs makes the outcome much clearer.
It is very probable that Germany had spies in Coventry, who would inform their government beforehand as to whether or not Britain was making a move to defend the city against attack.
Strangely enough, German espionage would have little effect on the payoffs, even though this would provide Germany prior knowledge of Britain’s action. If Germany were to attack a defended Coventry, all would be the same as in the previous case, for Britain would realize that whether or not Germany had known about their decryption of Enigma earlier, they would know now. The major—in fact, only—change in payoffs comes from the (Defend, Refrain) strategy. If German spies noticed that Britain was preparing to defend Coventry, Germany could call off the raid. Theoretically, such a move might seem suspicious and lead the British to be aware that Germany was aware of the Enigma decryption. Even if this weren’t the case, though, all strategies would remain the same, since the payoff from (Defend, Refrain) would always exceed that from (Defend, Attack). Essentially, if Britain defended, it would be in Germany’s best interest to refrain, and if Britain deserted, it would be in Germany’s best interest to attack. Faced with a choice between payoffs of –105 for defending and 150 for deserting, Britain will clearly choose to desert.
Finally, we consider the case in which Germany has the ultimate informational advantage, knowing that Britain has decrypted Enigma without Britain’s knowledge.
If Britain defended, the payoffs would be the same, since Britain would realize at that point that Germany knew of the Enigma decryption. But if Britain thinks that Germany is unaware of the Enigma decryption, Britain will desert, so the Defend strategy is irrelevant. If Britain deserts, however, then they will still be under the assumption that Germany is ignorant of Enigma’s decryption, and this will be severely detrimental to Britain. If Britain deserts, Germany will be aware of the Enigma decryption without their knowledge whether Germany attacks or refrains, but Germany receive 50 more points from attacking, so that would be the preferable choice.
By this point, a clear pattern has emerged. If Britain were only concerned with Coventry, it would be in their best interest to defend against the attacking Germans, but in all the cases that take the future into account, the rollback equilibrium was (Desert, Attack), and this was also the outcome if Britain never decrypted Enigma. Not wanting Germany to be aware that they have cracked the Enigma code, it is in Britain’s best interest to take the action that would seem to indicate that they are oblivious to Germany’s plans. And, knowing that Britain will desert Coventry, it is always in Germany’s best interest to attack the city. Although the optimal choice of strategies has proven to be the same regardless of the circumstances, the payoffs vary greatly, and they are based on which country is one step ahead when it comes to information. The party with the advantage wants its opponent to get the impression that nothing is any different, and that is what this entire situation boils down to. Since the Allies won the war, it is safe to assume that Germany never suspected Enigma’s secrecy had been breached. In fact, Project Ultra and its accomplishments were probably the single most important factor leading to Britain, the United States, and the rest of the free world triumphing over Nazi Germany.
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West, Nigel. A Thread of Deceit. New York: Random House, 1985.
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