Ugly implications of a beautiful mind

Thanks to the World Congress of the Game Theory Society at Bilgi University, this week Istanbul is hosting four Nobel Prize winners in Economics. 

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 Prisoner’s Dilemma: 

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.