Monday, April 22, 2013

Nash Equilibrium and Tipping Point

Nash Equilibrium is one of those juicy ideas that sticks in one's mind. It can be explained wonderfully with  simple examples, and it holds the promise of even working in very complex scenarios.  One possible extension to the idea of Nash equilibrium is the idea of adding a probabilistic basis to decision-making. As in, for the famous prisoner's dilemma question, what if each prisoner evaluated his decision after attaching a vague probabilistic metric to the other prisoner prizing loyalty over a beggar-thy-neighbour policy? That could be fun.

I must warn that there is no academic basis to this line of thought. Random pontification was never inhibited by mere lack of academic basis. So, here goes.

In the prisoners' dilemma game, prisoners are expected to base their response on how the fellow-prisoner has taken his/her previous decisions. So, arguably if we allowed for this kind of scenario where everyone takes decisions based on how others have done, we approach a pseudo-intellectual basis for the other popular idea - a tipping point. Somehow loyalty begets loyalty, self-interest begets self-interest. And beyond a point, exception becomes norm and vice versa.

From society's point of view, it is in the overall interest that the Nash equilibrium be avoided, as it is collectively sub-optimal. However, if individuals reach a level where they worry only about themselves, we would inevitably land at the Nash equilibrium. the momentum for the tipping point can be either way. So, society has to perhaps create levers that give momentum for the trend away from the Nash Equilibrium.

Let us take a simple example to see the basis for this. In Chennai, at every traffic signal, we have what I am going to refer to as the ungentle-creep. When a signal reads red, all vehicles start behind the stop line. But, slowly, inexorably, all vehicles start inching up every second until they finally reach a point where they severely constrict the flow of traffic for the lanes that currently have the green-signal. There is a belief that if this inching-up is not done,  the lane that currently has green signal will have a bunch of guys squeezing through even after 'their' green turns to red (because they can). So, in order to defend a narrower set of interests, everyone has to opt for the collective sub-optimal solution.

The traffic in Chennai has reached this blissful Nash equilibrium at many levels.

Perhaps a great time for an external agency to provide an incentive for the system to go towards the other tipping point. Not likely in my lifetime. :-)