Thanks to the World Congress of the Game Theory Societyat Bilgi University, this week Istanbul is hosting four Nobel Prize winners inEconomics.
John Nash, who was played by Russell Crowe in A Beautiful Mind, is speakingwith three other fellow laureates today at the appropriately-named Nobel Panel.Nash is one of the forefathers of modern game theory and developed the conceptof “Nash equilibrium”. The idea can best be illustrated by the canonicalPrisoner’s Dilemma:
Footballers Alexander and Abraham are arrestedas part of a match-fixing investigation. The prosecutor puts them inseparate rooms and offers them the same deal: If one testifies against theother, the rat goes free and the other gets a five-year sentence. If bothremain silent, they each receive a one-year sentence. And if both decide totestify, each is handed a three-year sentence.
Nash equilibrium is a set of strategies, where noplayer has anything to gain by changing his own strategy unilaterally. In thisgame, the equilibrium outcome is both men testifyingbecause each footballer can be better off by ratting regardless of what theother does. However, they would have been better off had both remained silent.
Bank of America strategists David Woo andAthanasios Vamvakidis have applied theconcept to the Eurozone. Keeping the payoff structure the same, theyreplace the footballers with Germany and Greece, with the former’s optionsbeing Eurobonds and No Eurobonds, and the latter’s Austerity and No Austerity.The two countries will not cooperate in equilibrium, meaning that Greece willnot undertake austerity and Germany will not OK Eurobonds.
This simple construct ignores many real-lifecomplications, but it does capture the main problem that neither side is ableto pre-commit credibly to the solution that would make both better off (Austerity,Eurobonds). Note that fiscal union would be the enforcement mechanism thatwould ensure each country lived up to is promises.
Woo and Anthanasios then calculate the costs andbenefits of a voluntary exit from the Eurozone for the major core and peripherycountries. They try to estimate the chances for an orderly exit as well as the impacton growth, borrowing costs and the country’s balance sheet following an exit.
Their analysis is only a simplification, but theresults are striking. First, while everyone is expecting Greece to exit first, Italy and Ireland havethe highest incentives to leave. Italy has a good chance of an orderly exitand stands to benefit from competitiveness, growth and even balance sheetgains. On the other hand, while it is the country most likely to achieve anorderly exit, Germany has the lowest incentive to leave, as it would sufferfrom lower growth, higher borrowing costs and a negative balance sheet effect.
Using these payoffs, the strategists then devise athree-period game, where Italy first decides whether or not to exit. If itdoesn’t, Germany could pay her to stay and then Italy again answers thequestion, “should I stayor should I go”. The Nash equilibrium of this game is for Italy to exit inthe first period.
It seems, therefore, that game theory does notpredict a bright future for the Eurozone.