Spy Games and Rationality
July 30, 2013
I like studying spy games because they are great examples of subtle rationality. Rationality is really hard. Rationality in the context of other rational agents is even more difficult. Add to this the fact that you don’t know all the moves of the game or what the other players know, and you’ve got a really interesting situation, rationally speaking. The best way to get a handle on really interesting situations is to look at a bunch of examples. If these examples involve espionage, everyone wins.
Game theory normally makes an assumption that all players are perfectly rational with complete information about the game, and that these things are common knowledge. But these assumptions are never true about humans. If you relax these assumptions, you get games of incomplete information in which player rationality is bounded. That is, you get more realistic games with more realistic players.
In spy games, we have realistic examples of boundedly rational players working with incomplete information, with an additional catch: the players are actively trying to deceive each other. This leads to some really beautiful lessons about strategy in what I’ll call adversarial epistemic environments. An epistemic environment is adversarial when it is possible to actively mislead other players through deception and misinformation. So, real life. I’ll refer to rational decision making in these environments as adversarial rationality.
Let’s look at a cool but horrifying example. We can’t be sure about the veracity of this account, because it has been both asserted and denied by actual British spies from the time period, but we’re only interested in the strategizing involved, so the veracity is irrelevant.
During World War II, the British hired a bunch of mathematicians and put them to work breaking the German Enigma cryptosystem. The mathematicians, including Alan Turing, succeeded in their task, by constructing a decryption machine called the Bombe. The Bombe decoded some Enigma traffic to the Luftwaffe indicating a raid on the British city of Coventry. Churchill, in his strategic wisdom, ordered that no defensive measures be taken against the raid. Coventry was all but destroyed. When the Nazis achieved similar levels of destruction in future raids, they used the word “coventried” to describe them.
In this example, we have an interesting game. Churchill knows that he’s broken the Enigma code, and the Nazis don’t know this. Churchill knows that the Nazis don’t know that he’s broken their code. This is an information advantage, because Churchill is one “knows that…” step ahead of the Nazis. However, if Churchill had prevented the Coventry raids, the Nazis would have known that he’d broken the code. Thus, in order to maintain an information advantage, Churchill had to make a large tactical sacrifice.
Winston Churchill and the Cigar of Rationality
Churchill’s First Lesson: Make a big tactical sacrifice to keep a big information advantage.
Regular old game theory is insufficient for modeling this situation, because the players are trying to deceive each other. Churchill has an information advantage over the Nazis, and in fact his strategy turns on keeping this advantage. In regular game theory, this advantage can’t even exist.
But it was an advantage. Churchill judged that it was worth the lives of thousands of his citizens. How could this be true? The attack happened in 1940, long before the Allied forces had a clear tactical path to victory. It’s not as if Churchill sacrificed his citizens because he knew that in only a few moves he could wipe out the Nazi forces. Victory was not guaranteed, given his move. It’s just like in chess, when you sacrifice a pawn (or two) in the opening game because you want to keep control of the center of the board. It’s not like at that point in the game you have a clear sequence of moves in mind to achieve checkmate. You just know that maintaining control of the center is a good position to have later on.
This tells us something about the difference between strategic moves and tactical moves in games with boundedly rational agents. A strategic move maintains or establishes a positional advantage that in itself confers no direct payoffs, but only promises good opportunities to take advantage of it later in the game. A tactical move directly confers payoffs. Tactical moves seek to win battles, while strategic moves put you in a position to win wars. For chess aficionados, this distinction is called tactical vs. positional play. That’s what Churchill had in mind. The sacrifice of Coventry corresponded to a strategic move in which he maintained the information advantage over the Nazis regarding the Enigma machine.
Churchill’s Second Lesson: Achieve and keep an information advantage by breaking the other player’s vanilla rationality.
Churchill was taking advantage of the fact that vanilla empirical reasoning (updating beliefs according to Bayes’ Theorem) is a bad guide to rationality in adversarial epistemic situations. The Nazis, in observing the successful attack on Coventry, would reason as follows: It is very unlikely that the Enigma code has been broken (in fact they thought it was impossible), and if Churchill had broken the Enigma code, it is very very likely he’d have prevented it; the overall likelihood of Churchill preventing it is small, but much bigger than the likelihood they broke the code. Therefore, given that the attack succeeded, the chance they’ve broken the code is very very small.
That is valid Bayesian reasoning. Churchill broke the Nazis’ valid Bayesian reasoning by providing them with the misinformation they needed in order to maintain the false belief that the code was still not broken. As far as regular rationality goes, in non-adversarial epistemic environments, the Nazis reasoned correctly. Churchill wanted to make sure that they reasoned correctly all the way to his intended false conclusion: that he hadn’t broken their code.
I think this is one of the most interesting and important aspects of strategic reasoning. It’s the type of stuff that wins wars and Poker games. While not all of us find work as spies and Poker stars, we all engage in some form of strategic interaction involving deception.
Churchill’s Third Lesson: Adversarial Rationality is all about getting and keeping the information advantage.
The British invested a lot of their resources into intelligence gathering, and they were much better at it than the Nazis. America learned how to play the intelligence game from the British, and many of the Allies’ advantages were the fruits of this labor.
Of course, the Nazis also had spies, and they were spending resources trying to figure out what the British knew. Why didn’t the Nazis devote more resources to intelligence gathering? Maybe they could have reclaimed the information advantage. They could have made the epistemic situation like this: The Nazis knew that Churchill had broken the code, Churchill didn’t know that they knew this, and the Nazis knew that he didn’t know.
Heh, well, the British had an operation called Double Cross, in which they caught Nazi spies and turned them into double agents. So, the Nazi’s spies would issue reports consistent with Churchill’s story that the code had not been broken, thus giving the Nazis even more misinformation supporting their false belief. Every step of the way, Churchill played to gain and keep the information advantage, which ultimately led to a successful D-Day invasion.*
* I appeal to Blogger’s License and dramatically condense history into a naively simple narrative in order to illustrate a point.
About the Author: Seth KurtenbachSeth Kurtenbach is pursuing his PhD in computer science at the University of Missouri. His current research focuses on the application of formal logic to questions about knowledge and rationality. He has his Master's degree in philosophy from the University of Missouri, and is growing an epic beard in order to maintain his philosophical powers. You can email Seth at Seth.Kurtenbach@gmail.com or follow him on Twitter: @SJKur.
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