May 29, 2015

Game Theory, Nash Equilibrium & Grexit

John Nash died last week. Someone asked me about the significance of his work and the so-called Nash Equilibrium & Game Theory which won him the Nobel Prize. It made me think a while.  Lot of economic theories are just theories with very little practical applications. Is this game theory like that ? 
Much of the geo-political situations , competitive decisions in many industries can be modeled by applying game theory principles. If you model the problem correctly, this can give you pretty good insights into your competitor's strategy & give a lot of structure & logic to your decision making . I could think of no better example than the looming possibility of Greek default & subsequent exit that media has labelled as the Grexit question
But before that, how do you translate / model a problem into a Game Theory situation where we can apply the Nash Equilibrium principles . I stumbled upon a structured approach illustrated very well here 
Its important to understand the modelling part here . You need to model the Co-operate / Not Cooperate aspect into strategies / positions here. You maybe tempted to model Greece's strategy as 'Default on Debt' / 'No Default'. But that,s actually the result of a competitive position , not the position in itself. And once you have modeled the competitive strategies, you need to assign pay-offs ( which can be just a relative number ) to those .
These payoff values are debatable. But as long as those are relatively OK, that serves the purpose ( unless you are getting into the next level of probabilistic calculations there ) 
Now, Identify Greece's best strategy to EU's ' Restructure the debt'  position. That is always to do the fiscal reforms. If you don't do the fiscal reforms, you tend to risk EU's co-operation, potentially fail to repay further installments etc 
What's Greece's best response to EU's 'No restructuring stance'  ? It is still to do the fiscal reforms as unless they do that, they risk defaults, potentially fall out of Euro.
Whats EU's best response to Greece's 'Do the fiscal reform' position ? Their best response is to do the restructuring as, if they don't do that, Greece may still default on its debt inspite of fiscal reforms and  EU / IMF may miss further repayments
EU's best response to Greece's 'No reform' position ? A grexit is a position that everyone wants to avoid at all costs. So, EU's best response is still to restructure the debt so that Greece can continue to pay the reduced debt interest & continue to be in Euro  
So, where do the strategies overlap in ?  Do the reform, Do the re-structure column.  Greece has played its part very cleverly till now. They have made the repayments so far, they have tried some reforms. They are trying to nudge EU & IMF into the Co-operate proposition now. We'll get to know by June - 5 & may be later in the month, whether they reach a ' Co-operate Co-operate' position 
Now, what does John Nash say ? " Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy"
So, if they reach a Do the reform - Do the restructure position, no side has got anything to gain by moving off into a different position subsequently.
Let's see how it turns out ! 


Rahul said...

Very nice Ajith! However, what is the impact of the exact values your are assigning to the various payoffs and costs, on the equilibrium? In the case that none of these values can be established, is this analysis still useful?

Ajith Prasad Balakrishnan said...

I'm not yet into the entire maths part :) . From what I understood, if you get the exact payoffs right, you can measure the sensitivity / stability of the equilibrium position. Also, I think it is used in advance levels of option pricing as well.

From a conceptual level, it should be useful to people who are working on competitive strategy.. Like, if you know that you are in a Nash Equilibrium, for you to move towards a different position., both you and the other party needs to change strategy together.

Maybe I need to talk to practitioners more :)

Anonymous said...

I think this is an interesting approach. I don't know much about the maths part here either. Post again if you work on it further :)