For Italy, It Is Game Theory Over

Tyler Durden's picture

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

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LULZBank's picture

It will be all well by Monday.

I think I need to buy a gun's picture

The fourth turning is definitely here bitchez

flacon's picture

Well.... I agree... more QE and/or more LTRO = a market crash.... so the only thing they have left is their VOICE... which incedentally is what Bernanke SAID when questioned about what is left... he said "communication".... fuck you vocal chords, you stood your husband up once too many times and now he is saying "Go fuck off!". Viva la 2011!

Freddie's picture

The EU-SSR and Euro need to go - along with our islamic in November.

FreedomGuy's picture

He who exits first exits best.

dark pools of soros's picture

He who exits first gets to the next party quicker

battle axe's picture

Somebody exit something, this has now gone past tedious to fucking coma inducing boredom.....

Hype Alert's picture

It's broken.  The market runs on headlines, not data.  So End Game is the ultimate WIN.  Think of the printing they will justify jawboning now.


Not that anything other than printing matters:

Lachman: Europe’s Perfect Economic Storm Could Drench the U.S. Presidential Election

flacon's picture

There comes a point where printing makes the market go DOWN, not up. And we are there now. Too many premature ejactulations and they are limp... it is time to shot the hell out of this fuck because there is nothing left. Krugman can save the day by convincing the Fed to print TWENTY TWO THOUSDAND MILLION DOLLARS but .... even so... it's money in a wheelbarrow now. It's cooked. Done. Toasted. 

Hype Alert's picture

Remember Zimbabwe?

 Check out their stock market. 


Here some charts on Weimer's market.

yogibear's picture

The DOW going up like that would make Krugman, Bernanke, Greenspan, Yellen and Dudley extremely happy. CNBC's guest would be throwing celebrations for each 10,000 additional points added. Missing would be the damage being done  in the underlying economy being reported. The Fed is on a kick to keep the stock market going up with the wealth-effect mindset.

Hype Alert's picture

Who knows, maybe we're on our way to a Zimbabwe or Weimer market now.  I hope not, but we do know it's not based on fundamentals.

Printing is a spiral and either they want it to get out of hand or they are so arrogant they think they know better and anyway the why is really not important.


The debt was created by spending and printing to pay off that debt will only increase the cost of things that was the spending was on in the first place. The spending will continue and so will the debt and then so will the printing. Get it? Spiral. Every cost we know of is expected to go up; health care, energy, food, etc. and that's because of demand. Add in printing and we're going to have a problem. Add in the destruction of baby boomer retirement accounts and their health care will certainly fall on the rest of society. They can paint the market higher with gimmics and bs, but it solves nothing. It just fans the flames of the problem.

Freddie's picture

I said on the day the Democrats elected, you know who in 2008, that he was Mugabe 2.  Nice job you fukkks who voted for Muhammed.  McCain sucked less but is also a POS.

lewy14's picture

I disagree about "fundamentals". If you have a claim on some real assets with even the potential to create an earnings stream, then you have something of fundamental value. This is equity - "the stock market".

If you have cash, you have claims on faerie farts. This is "fiat currency".

So yes, the advances in the stock market are based on "fundamentals".

Consider that perhaps currency destruction is, even now, being priced into the equity market, which will confuse the hell out of the bears, and give false assurances of normality to the regime supporters.

boogerbently's picture

Two possible theories for gold.

Leaving the Euro, countries will need their own currency, it will have an uncertain value unless based on gold.

Gold rises.

Uncertainty about the Euro and new currencies forces investors to the dollar.

Gold falls.

lasvegaspersona's picture

Maybe it is a different game they are playing than the one that appears it to be.

flacon's picture

Where can I buy rubys? Rubys? Where can I buy ruby slippers? Red slippers? Red?! Oh..... shit they told the story wrong... it's SILVER slippers! 

FreedomGuy's picture

Game theory and Nash-equilibrium do not assume coercion.

disabledvet's picture

ABSOLUTELY true. What's going on in the EZ is neither a game nor theoretical. Time to lower the boom and monetize. "Anyone who gets out of line will realize who's in charge." not promoting this of course...but human believe in BLAME theory not game theory.

LongBalls's picture

Get out. Listen to your gut. Cash out now while you can.

LongBalls's picture

All you need to understand is one very simple point. When markets hinge on one person or a small group of person's as to whether or not they will perform any single action to prevent it from tanking; then free markets are dead and risk is VERY HIGH.

Markets are now 100% controlled and depend on a very, very, very small group and class of people. Beg for it or vacate. I choose freedom.  

Jason T's picture

Game theory over

    Insert Coin

Buckaroo Banzai's picture

To keep playing for 3 more months, insert $700 billion in 10...9...8...7...6...5...

Manthong's picture

Get me some of that cheap tail..?   risk?

..or pass on the skank?

Zola's picture

I just stopped reading when i saw the "benefits" they give to the Eurobonds/ no Eurobonds. Rubbish

fonzannoon's picture

cnbc saying ecb gonna peg spain's ten year at 5%

fonzannoon's picture

but libor is bad

JustObserving's picture

The solution will be to print.  If the US with much larger deficits to GDP ratio can have ten year bonds at 1.4%, why cannot the Eurozone do that?  Draghi has to agree to buy bonds if interest rates exceed 5%.   Magically, all interest rates will be below 5% by Monday and Europe will be fine.

Look at the UK.  It is in a recession and its borrowing costs are less than a third of Italy and Spain.  The only advantage it has that it can print money into existence.

Why is taking Europe so long to see the obvious?  Print, print, print.  Print before Spain and Italy become Greece.  Print now.  Get gold to $2000 and silver to $45.

yogibear's picture

The only solution they have now is to print. The boxed themselves in.

Piranhanoia's picture

If Italy defaults, and prints a gold backed lire, they should do quite well.  Will their payments be extended again?

debtor of last resort's picture

Aka what came first, the chicken or the egg.

ddtuttle's picture

This is too tame a set of scenarios.  The real dilemma is that Germany will be forced to default if they stay in the Euro (the whole EU will default even after Germany bankrupts itself trying to save it).  If they leave teh Euro they probably have the where-with-all to save their banks and not default.

Of course, the Euro would have to devalue massively, but that's exactly what the PIIGS & France need.

Everyone assumes the new Deutsch Mark would appreciate making BMWs and Mercedes too expensive.  However, they Germans would have to print a large number of DMs to bail out their banks which would have just lost their shirts on EU sovereign bonds.

Actually I don't belive the EMU without Germany would survive very long, but it might work for awhile.

ddtuttle's picture

This is too tame a set of scenarios.  The real dilemma is that Germany will be forced to default if they stay in the Euro (the whole EU will default even after Germany bankrupts itself trying to save it).  If they leave teh Euro they probably have the where-with-all to save their banks and not default.

Of course, the Euro would have to devalue massively, but that's exactly what the PIIGS & France need.

Everyone assumes the new Deutsch Mark would appreciate making BMWs and Mercedes too expensive.  However, they Germans would have to print a large number of DMs to bail out their banks which would have just lost their shirts on EU sovereign bonds.

Actually I don't belive the EMU without Germany would survive very long, but it might work for awhile.

JustObserving's picture

"The real dilemma is that Germany will be forced to default if they stay in the Euro"

Why?  Europe is in much better shape in terms of deficits and debts than the US and the UK. Why should Europe default? 

Europe can commit financial suicide by refusing to print when everyone else is printing.  Why are UK ten year bond yields a quarter of Spain's?  

If everyone else is printing, it is suicidal not to print.  Bond holders just want their principal back even though it may be in just minted money.

What is the US doing constantly? Printing.  When it is not QE, it is Operation Twist - an indirect method of printing money by keeping long term interest rates low. This continuous printing has greatly benefited the US while Europe struggles to survive under ever increasing interest costs.

wagthetails's picture

The mother of all deal fatigue indeed.

Although I too think nothing will be done, the difference between the model and the prisoner's dilemma is that Germany and Greece can actually talk to each other before making a choice.  that is the risk to this analysis, they actually communicate. 

I still don't think there will be an agreement, but more because Germany will never agree...if it was only Greece, it they would agree...but soon after Greece, the others will line up.  They have to take a stand. 

Adding further pressure is that the EU has already reached the point of no return: too much time has passed and now it is very political in each country.  An agreement would work if done immediately (like TARP), before the common citizen has learn enough about it to be outraged.  But at this point, all Greeks and all Germans will prevent their government from ever compromising.  the drama of the MSM and extremist will only harden nationalist (to the point of isolationist) views. 


PontifexMaximus's picture

I told you before, that it's a matter of less than 3 months, that ESM or ESFS will have bank status and therefore can get financing by Mario himself. Problems solved and the Anglosaxon HF crowd has to look for other opportunities to make a few bucks. Euro bashing game and all collateral games will belong to the recent past, watch out for your bonuses.

Gromit's picture

Beggar your neighbor.....let the currency wars begin!

buzzsaw99's picture

they will chickenshit halfass their way through it. imo germany wants an artificially weak currency to help their exports but they don't want to get there by giving a shitload of euro to the piigs to spend. if they use dm then they can buy usd and not have to bail out the pigs and get the same result.

Tao 4 the Show's picture

Major flaw in this analysis: it assumes perfect coupling between the county's interests and the actions/decisions of the leaders. Obviously, this is a fallacy. The leaders are engaged in a game theoretical construct of their own, and their country's best interests are far, far down their priority list. Who believes Goldmanite Monti is representing Italy's best interests?

GCT's picture

Historically governments always print.  Printing delays the math but makes the pain devastating and has throughout history.  We never learn.

engineertheeconomy's picture

Historically, evil governments always print paper and steal, good governments have always been on the Gold Standard

SmittyinLA's picture

Game theory doesn't work when playing with Wookies

Yen Cross's picture

  I have read this post "10" times over.  I can't argue it in a definitive way.  

   BOOT Kicks can > Cypress, and other ( sovereigns)...  

  The head of the ECB has gone rogue. Draghi is incompetent!

        A true diplomat would parlay his constituents.  Merkel walked away with a bailout plan. She just wants to melt the butter!