Game Theory is a useful tool for analysing Europe's crisis. Bank of America dedicated a full report to a game theory scenario on the Euro Breakup, analysing the costs and benefits of a voluntary exit from the Euro-area for the core and periphery countries. The results are shocking.
Italy and Ireland (not Greece) are expected to exit first (with Italy having a decent chance of an orderly exit) and while Germany is the most likely to achieve an orderly exit, it has the lowest incentive to exit the euro-zone - since growth, borrowing costs, and a weakening balance sheet would cause more pain.
Ultimately, they play the game out and find out that while Germany could 'bribe' Italy to stay, they will not accept and Italy will optimally exit first - suggesting a very dark future ahead for the Eurozone.
The cost of insuring against EUR tail risk, which was already in retreat even before the EU Summit, has fallen further since, is at 2 year lows.
One of the most provocative observations of modern game theory is that the most likely outcome is not always the optimal one. Put differently, the dominant strategy for game players is not always to cooperate, even when everyone is better off if they do.
The most famous illustration of this is the Prisoner’s Dilemma. In this game, two men are arrested. The police offer both men a similar deal. If one testifies against the other, and the other stays silent, the betrayer goes free while the one who remains silent gets a one-year sentence. If both remain silent, they will each get a one-month sentence. If both decide to testify against the other, each will get a three-month sentence. Even though both will be better off if they stay silent, the “Nash equilibrium” is that both men will testify against each other. This is because from the perspective of each prisoner, regardless of what the other person does, he can be better off by betraying.
The prisoner’s dilemma problem can help us better understand the dynamics of the eurozone crisis.
Below (Table 1), we
present a highly abstract, stylized form of the game that Germany and Greece have been playing for the last two years.
Greece is given two options: austerity or no austerity. Germany also
has two options: Eurobonds or no Eurobonds. For each of the four
possible outcomes a certain payoff is assigned for each country that is
meant to be illustrative, but captures the essence of the different
political/economic considerations of the two countries.
As the payoffs in Table 1 imply, both countries would fare better if they choose to cooperate (Greece agreeing to austerity while Germany agreeing to Eurobonds) than if they do not cooperate (no austerity and no Eurobonds). However, Greece would be even better off if it chooses no austerity but Germany agrees to Eurobonds. Similarly, the best outcome for Germany is that it opts for no Eurobonds but Greece chooses austerity. We assume that neither country knows what the other country is going to do before it has to decide on a course of action.
It is easy to see that the Nash equilibrium is no austerity and no Eurobonds (uncooperative equilibrium). This is because from the point of view of Greece, regardless of what Germany chooses, it will be better off if it opts for no austerity. Similarly, from the point of view of Germany, regardless of what Greece does, it will be better off if it chooses no Eurobonds. As with the Prisoner’s Dilemma, no austerity and no Eurobonds can be shown to be the Nash equilibrium even if we were to allow for the game to be played repeatedly.
The fact that the dominant strategy for both countries is not to cooperate is why now more than two years into the crisis Greece is not closer to implementing a credible reform program and Germany is not any closer to agreeing to Eurobonds.
The obstacle is that neither side is able to make a credible pre-commitment to doing the “right thing,” to the extent that there is no enforcement mechanism to ensure that each country lives up to its promises.
The lack of an enforcement mechanism is why the Germans are demanding that fiscal union will have to precede Eurobonds. Fiscal union, by taking fiscal policy out of the hands of the national governments, solves the pre-commitment problem. However, very few eurozone countries are willing to entertain the notion of giving up their independent fiscal policy, especially given that, as members of the monetary union, they do not have recourse to an independent monetary policy.
If the eurozone is no closer to a fiscal union and Eurobonds, we need to consider other potential outcomes of the crisis. Much has been said about involuntary exit from the eurozone , but what about the chances of a voluntary exit, meaning a country (or multiple countries) opting to call it quits on its (their) own accord?
A decision to stay or exit should be dictated by a cost and benefit analysis. What are some of the considerations that should go into such an analysis? There are four key questions that will have to be answered before any such decision can be made:
What are the chances for an orderly exit?
What is the impact on growth following an exit?
What is the impact on borrowing costs following an exit?
What is the impact on the country’s balance sheet following an exit?
Two very interesting results emerge:
Even though much of the market focus on exit risk has been on Greece, Italy and Ireland have the highest relative incentive to voluntarily exit the euro, by our analysis. In the case of Italy, it faces a relatively higher chance of achieving an orderly exit and it stands to benefit significantly from competitive gains, growth gains and even balance sheet gains. No wonder former Prime Minister Berlusconi has been recently quoted as saying that leaving the euro is not a “blasphemy.” Among the peripheral countries, Spain appears to have the lowest relative incentive to leave.
While Germany is the country most likely to achieve an orderly exit from the Euro, it also has the lowest incentive of any country to leave. It would suffer from lower growth, possibly higher borrowing costs, and negative balance sheet effect. Austria, Finland and Belgium don’t have strong incentive to leave, either.
Can Germany “bribe” Italy to stay?
Incentive to leave the euro varies from country to country. Among the major economies, Italy stands the most to gain from exiting, whereas Germany has the most to lose from exiting. Germany would also lose from the exit of other countries. (Say Italy leaves the euro but Germany stays. German holdings of Italian liabilities would fall in value, German exports to Italy would suffer and German companies would now face more competitive Italian manufacturing firms.) Does this mean that Germany would be willing to pay a price for Italy (as it has for Greece, Ireland, and Portugal) to stay in the euro? The answer is Yes but would Italy accept it.
What is the Nash equilibrium of this game?
Italy is clearly better off exiting than staying (after Germany has already paid the “bribe”), as the payoff for Italy in outcome 4 is inferior to the payoff in outcome 3. If we can see this, so can Germany in period 2. Whether it pays or not, Italy will exit in the following period. Therefore, Germany is better off by not paying. Now in period 1, Italy can make the informed calculation that Germany will not pay. This means that Italy has an incentive to exit in period 1. The bottom line is that the only stable equilibrium of this game is that Italy exits the euro and, more importantly, it exits already in period 1.
This game and the analysis in the previous section would suggest that we should not expect what has already happened between Germany and Greece during the eurozone crisis to play out the same way for Italy if the crisis spreads. Italy has more incentives than Greece to voluntarily exit the eurozone, in our view, while it will be more expensive for Germany to keep Italy in the eurozone. This means that Italy could be even more reluctant than Greece to accept tough conditionalities for staying.
Only a weak Euro can save the Eurozone
Despite the depreciation of the euro in the last three years, it is still nearly 10% stronger than where it was in 2000. Against the USD, it is still 45% stronger than its low in November 2000.
A much weaker Euro would significantly reduce the incentive of any country to exit. For example, a 20% depreciation of the EUR against the USD would reduce by nearly half the loss of competitiveness of Italy to the US since the inception of the Euro.