Greece Plays Colonel Blotto With Europe
Greek officials are flying around Europe this week, trying to talk to their counterparts in different countries instead of the “troika” of the International Monetary Fund, European Central Bank and European Union that had been their negotiating partner up to now.
Why would they do this? One explanation can be found in a game known as Colonel Blotto. In Colonel Blotto, adversaries allocate troops across multiple fronts. Whoever has the most troops on a particular front wins that battle, and whoever wins the most battles wins the war.
If each side goes to war with the same number of troops, Colonel Blotto is a frustrating game that no one can reliably win. If one side has more resources than the other, though, things get interesting. It turns out the weaker side has a clear interest in increasing the number of fronts.
To illustrate, consider a Colonel Blotto game where one side has 50 soldiers and the other 33. If there is only one front, the outcome is certain -- 50 is more than 33. If fighting expands to three fronts, the stronger side can still achieve certain victory by allocating 17 soldiers to the first front, 17 to the second and 16 to the third. The weaker side can win one front, but then wouldn’t have enough troops left to win either of the other two.
Spread things out over five fronts, though, and this certainty vanishes. If the stronger side simply puts 10 soldiers on each front, the weaker one can win by allocating 11 troops to three fronts and none to the other two. Every other possible allocation by the stronger side can be beaten as well. Most of the time it won’t be -- it’s still better to have 50 soldiers than 33 -- but for the weaker side a hopeless effort has been transformed into one that can succeed.
There are clear echoes of this approach in the new Greek government’s attempt to shift the negotiations away from a single powerful adversary to multiple ones. Colonel Blotto also helps explain why German Chancellor Angela Merkel and Dutch Finance Minister Jeroen Dijsselbloem, the chairman of the euro-area finance ministers group, are trying to keep discussions on a single front.
Blotto doesn’t explain everything, of course. It’s just an oversimplified model. But game theory does illuminate a lot about high-stakes negotiations. That is probably even truer than usual for these particular high-stakes negotiations, given that Greek Finance Minister Yanis Varoufakis once co-authored a book titled “Game Theory: A Critical Introduction.”
One game that Varoufakis devoted much energy to in his academic career is what’s called the Prisoner’s Dilemma. In the Prisoner’s Dilemma, two suspects in a crime, let’s call them Al and Bill, are taken off separately for questioning. The police tell each of them that:
- If both rat on the other, they’ll get two years in prison apiece.
- If both are silent, they’ll get one year in prison apiece.
- If Al rats on Bill but Bill is silent, Al goes free and Bill gets five years in prison. (And vice versa if Bill rats and Al is silent.)
The expected outcome of this game -- if Al and Bill are rational individuals who can’t communicate with each other -- is No. 1. Al can’t know whether Bill will rat on him or not, so he assumes the worst and protects himself by ratting on Bill. Same goes for Bill. Outcome No. 2 is clearly better for both, but under the assumptions of standard game theory, which are the same as the assumptions of standard economic theory, they just can’t get there.
Happily, though, when similar questions are posed to actual human beings, they more often than not land at outcome No. 2 or something like it. A sort of self-interested altruism turns out to guide lots of real-world behavior. This makes sense when you consider that most “games” in life are played not just once but repeatedly, giving people a chance to learn to behave in a way that gives them a better result most of the time. Varoufakis has done work that explains this mathematically (thanks to Steve Keen, the prominent critic of mainstream economics and a long-time friend of Varoufakis, for pointing me to it).
Greece’s negotiations so far with the EU, though, have repeatedly resulted in outcomes that leave both sides worse off. They have gotten stuck in a prisoner’s dilemma -- which seems all the more reason to try to shake up the negotiations.
The name does not appear to have a real-life antecedent; some guys at RAND just started using it in the 1950s. Also, pretty much everything I know about Colonel Blotto I learned from Scott E. Page's Coursera class, "Model Thinking."
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