Most people know the game of chicken. Two cars accelerate toward each other trying to intimidate the other into swerving – if neither swerves, both die a fiery death. There’s been talk that German chancellor Angela Merkel and the debt-ridden eurozone countries are currently playing this game. While this is a very helpful metaphor, it also tends to ignore the highly modified nature of the game they’re playing. If they were playing the classic version, no one would really care because compromise would be inevitable. But they haven’t yet compromised, and it’s possible they won’t. To better understand this, we need to modify the classic version to get the kind of strategies we’re seeing being played.
The classic game of chicken
As game theory describes chicken, there are two players each with two strategies, continue going straight or swerve. To continue is to play “courageously” while to swerve is to play “cowardly.” Of course if both players play courageously, they die. The classic version accounts for the terror of this strategy by awarding both players -100 points. If one player continues and the other swerves (these two possibilities, to use the jargon, are the pure strategy Nash eguilibria), then the continuing player gets 2 points and the swerving player gets -2 points. If they both swerve no one gets any points.
The problem with the pure strategies in any game of chicken is that each player wants to continue going straight while forcing the other to swerve, but who decides who’s going to do what? A bargaining situation develops wherein each player tries to convince the other to play their less-preferred equilibrium strategy. (This bargaining situation is where the eurozone members currently find themselves.)
Because each player could choose either strategy and still be in the overall game’s equilibria, the game has no “dominant strategy” – which is to say, neither player plays the same way 100% of the time. To figure out how to play we need to develop a “mixed strategy” solution. (Rock, paper scissors is a great game for understanding mixed strategies as it would be pretty stupid to play rock all day.) A mixed strategy solution is a way of playing the game that makes one player indifferent to their opponent’s strategy – it’s basically the correct probability of playing a certain strategy. If we do the math of classic chicken, with payouts of -100, -2, 0 and 2, the solution is that each player should continue 1 out of every 50 times the game is played, or 2% of the time.* This means that it’s extremely likely that both players will swerve because neither wants to risk getting -100 points, or a fiery death. The classic chicken model predicts that issues in the eurozone will get resolved.
A modified game of chicken
But what happens when we play around with the numbers (payouts) in an attempt to describe more accurately what’s going on? Classic chicken assumes payout symmetry and I’m not sure this is the case in geopolitics. It also assumes that because the relative payout for the death strategy is so terrible, players are massively incentivized to swerve. And I’m not sure this is the case either.
Let’s modify the game and use Germany (G) and Italy (I). Lots of assumptions will be made, but that’s what happens in modeling. Continuing for G means forcing austerity, policy restructuring and fiscal unity; swerving means issuing some kind of eurobond, or quantitative easing or more bailouts. Continuing for I means refusing austerity, restructuring and fiscal unity; swerving means accepting these things. The four possible strategies look like this, with my assumed outcomes and sometimes substituting the ECB for Germany (c=continue, s=swerve):
Gc : Ic – death strategy, break up of eurozone, disorderly defaults, etc. Gc : Is – ECB keeps monetary policy tight, a fiscal union forms, Italy reforms Gs : Ic – ECB loosens monetary policy, Italy gets debt write-down Gs : Is – ECB loosens monetary policy, Italy reforms, transfer payments happen
Regarding payouts, let’s imagine both still get -100 in the death strategy (neither wants the eurozone to breakup). If Germany continues and Italy swerves, Germany gets 50 and Italy gets -25. If Germany swerves and Italy continues, Germany gets -50 and Italy gets 25. And finally if they both swerve they each get -10. Basically, my modified payout structure attempts to account for the fact that Germany, as de facto head of the eurozone, has more at stake in the outcome of the game. We could play around with the numbers even more and come up with other versions of the game.
Using these numbers gives a very different picture of the probabilities at work. By altering the relative payout differentials and assuming Germany has more at stake, we come up with this strategy: Germany should continue roughly 55% of the time whereas Italy should only continue roughly 14% of the time.** And it seems that we’re seeing this kind of strategy playing out. Merkel and the ECB are refusing quantitative easing and enhanced transfer payments and demanding a kind of fiscal union, while Italy has already replaced a government with technocrats and begun restructuring.
A few final thoughts
The thing is, I actually think it’s more likely that Germany will “swerve” than my modified numbers predict. One way to account for this would be to give Germany fewer points if it continues and Italy swerves. This might more accurately represent the fallout if Germany continues enforcing strict monetary policy without increased transfer payments, even if Italy does reform. In effect, this strategy would represent more “punting” and the likely future consequences should be included in the model. But this is enough for now.
* Here’s the math. We set the utility of player 2 continuing equal to his utility of swerving. Player 2’s utility of continuing is some function of the probability of player 1 continuing. U = utility, P = probability of player 1 continuing, c = continuing, s = swerving.
U(2c) = P(-100) + (1 – P)(2) U(2s) = P(-2) + (1 – P)(0)
Then we set these two equations equal to each other and solve for P. The answer is the probability that player 1 continues. And it’s 1/50.
** Math is the same, only with different payouts used.