Thanks to the World Congress of the Game Theory Society
at Bilgi University, this week Istanbul is hosting four Nobel Prize winners in
John Nash, who was played by Russell Crowe in A Beautiful Mind, is speaking
with three other fellow laureates today at the appropriately-named Nobel Panel.
Nash is one of the forefathers of modern game theory and developed the concept
of “Nash equilibrium”. The idea can best be illustrated by the canonical
Footballers Alexander and Abraham are arrested
as part of a match-fixing investigation. The prosecutor puts them in
separate rooms and offers them the same deal: If one testifies against the
other, the rat goes free and the other gets a five-year sentence. If both
remain silent, they each receive a one-year sentence. And if both decide to
testify, each is handed a three-year sentence.
Nash equilibrium is a set of strategies, where no
player has anything to gain by changing his own strategy unilaterally. In this
game, the equilibrium outcome is both men testifying
because each footballer can be better off by ratting regardless of what the
other does. However, they would have been better off had both remained silent.
Bank of America strategists David Woo and
Athanasios Vamvakidis have applied the
concept to the Eurozone. Keeping the payoff structure the same, they
replace the footballers with Germany and Greece, with the former’s options
being Eurobonds and No Eurobonds, and the latter’s Austerity and No Austerity.
The two countries will not cooperate in equilibrium, meaning that Greece will
not undertake austerity and Germany will not OK Eurobonds.
This simple construct ignores many real-life
complications, but it does capture the main problem that neither side is able
to pre-commit credibly to the solution that would make both better off (Austerity,
Eurobonds). Note that fiscal union would be the enforcement mechanism that
would ensure each country lived up to is promises.
Woo and Anthanasios then calculate the costs and
benefits of a voluntary exit from the Eurozone for the major core and periphery
countries. They try to estimate the chances for an orderly exit as well as the impact
on growth, borrowing costs and the country’s balance sheet following an exit.
Their analysis is only a simplification, but the
results are striking. First, while everyone is expecting Greece to exit first, Italy and Ireland have
the highest incentives to leave. Italy has a good chance of an orderly exit
and stands to benefit from competitiveness, growth and even balance sheet
gains. On the other hand, while it is the country most likely to achieve an
orderly exit, Germany has the lowest incentive to leave, as it would suffer
from lower growth, higher borrowing costs and a negative balance sheet effect.
Using these payoffs, the strategists then devise a
three-period game, where Italy first decides whether or not to exit. If it
doesn’t, Germany could pay her to stay and then Italy again answers the
question, “should I stay
or should I go”. The Nash equilibrium of this game is for Italy to exit in
the first period.
It seems, therefore, that game theory does not
predict a bright future for the Eurozone.