For Italy, It Is Game Theory Over

We discussed the use of Game Theory as a useful tool for analyzing Europe's predicament in February and noted that it was far from optimal for any (peripheral or core) sovereign to pre-emptively 'agree' to austerity or Eurobonds respectively (even though that would make both better off). This Prisoner's Dilemma left the ugly Nash-Equilibrium game swinging from a catastrophic break-up to a long, painful (and volatile) continuation of the crisis. Recent work by BofAML's FX team takes this a step further and in assigning incentives and from a 'do-not-cooperate' Nash-equilibrium between Greece and Germany (no Greek austerity and no Eurobonds) they extend the single-period game across the entire group of European nations - with an ugly outcome. Analyzing the costs and benefits of a voluntary exit from the euro-area for the core and periphery countries, the admittedly over-simplified results are worrying. 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 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 and with EUR tail-risk so cheap, it seems an optimal trade - as only a weaker EUR can save the Euro.

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.

Should investors view these developments as a sign that the worst of the crisis is now behind us, or should they see them as providing an opportunity to pick up cheap EUR tail risk insurance? We would argue for the latter.

To some extent, the drop in tail risk premium is a reflection of the poor performance of tail risk hedges in the past two years. It is also possible that investors have reduced their exposures to eurozone assets so much that their need for insurance against EUR downside risk has simply diminished. We are skeptical about the wisdom of this consensus. Recent political developments in the eurozone have given us good reasons to think that the EUR breakup risk is not falling but rising

We employ game theory and a cost-benefit analysis to explain why in our view the market may be underpricing the voluntary exit of one or more countries.

Uncooperative outcome dominates

One of the most provocative observations of modern game theory is that the most likely outcome is not always Pareto optimal. 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, in our view. 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, we assign a certain payoff 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 (using backward induction) even if we were to allow for the game to be played repeatedly.

In our view, the fact that the dominant strategy for both countries is not to cooperate is why 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.

The economics of voluntary exit

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? In our view, 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?

These are all detailed in the paper below...

Final scores

To reach a final tally of the relative incentives that different countries are facing to voluntarily exit the euro, we add up the rankings across the above four criteria. For simplicity, we attach the same weight to each of our four sets of considerations. The results are in Table 6.
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, in our view. 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?

What we have established in the previous section is that the incentive to leave the euro varies from country to country. Among the major economies, we believe Italy stands the most to gain from exiting, whereas Germany has the most to lose from exiting. We would argue for the same reason that 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?

Yes, but we would argue that this strategy is not a stable Nash equilibrium. To illustrate this, think of the following game...

What is the Nash equilibrium of this game?

We can use backward induction to solve the game. In period 3, 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. If our inference turns out to be correct, this could have serious negative implications for markets in the months ahead.

Only a weak EUR can save the EUR

Despite the depreciation of the euro in the last three years, its trade weighted index is in the middle of its range of the last 30 years, and still nearly 10% stronger than where it was in 2000. Against the USD, it is still some 45% stronger than its low in November 2000.

Our analysis makes it very clear that a much weaker EUR may help save the EUR in the end. For one thing, a much weaker EUR 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 EUR (Chart 6).

Our analysis above suggests that the eurozone is now facing two paths – break up or accept a much weaker EUR. To the extent that the first path is likely to be also associated with a weaker EUR (at least in the transition), it seems that further depreciation of the EUR is inevitable.

Source: BofAML


Full document here - pdf