A Tribute to John Nash (A Beautiful Mind)

crowe-nash

It sounds like a Sport’s man dream.  A Person getting the Nobel Prize for his skill at analyzing games.  He was not a television Pundit or armchair critic of Manchester United or Chelsea, but an Economist.

John Nash, in Pop culture he is remembered as the man behind “A Beautiful Mind” and for the economists or specialists he’ll be remembered as a brilliant mathematician who won the Nobel Prize in Economic Sciences for his work on Game theory and the Abel Prize for his work on partial differentiation.

Nash Equilibrium is a game theory concept, so the general idea about this was it applies to games.  Economists had other ideas they use the word game a bit differently than Commoners, so you can think of a game simply as a scenario where more than one player interacts with other players and the payoff (results; perhaps who wins and who loses and by what margin) are determined by the decisions of all the players.  A simple game is played on “The Price is Right”.  The winner is the player who estimates the number closest to the value of the item without going over the original price.  All four players make a guess and therefore whether or not one player is a winner depends on the value of the item and the guesses of the other three players. In a similar way, rock-paper-scissors is a game.  If you throw rock, your result depends on what your opponent throws.

In a Nash Equilibrium, no player can increase his own payoff by deviating if everyone else keeps their move in same way. Another aspect of Nash Equilibrium that hurts brains is that there can be multiple Nash Equilibrium in one game. I am going to describe a two player game for simplicity.

Let’s Play a Simple Game

You and I get to pick an integer between 1 and 9 inclusive.  We do not get to communicate with each other about what we are going to pick.  Say that you pick a number by writing it down and giving the paper to the organizer. The results are as follows:  if we pick the identical number, then we each get paid similar number of dollars from the organizer.  If we pick different numbers then, each have to pay the same number of dollars as the number we picked to organizer

Initial payoff

I pick 3 and you pick 8.  Now I have to pay 3 and you have to pay 8.

Next payoff

we both pick 5.  Now we both get paid $5.

So what about the Nash Equilibrium?

The moves we made initially was not a Nash Equilibrium move.  If I were allowed to deviate, I would change my pick to 8 and we would both get paid $8 and vice versa. It only takes one of us wanting to deviate to make the scenario a non-Nash Equilibrium.  The moves we made in second situation was the perfect example of Nash Equilibrium.  If either of us were given the chance to deviate (given that the other player cannot change their move) then again neither of us would want to because we’d go from getting $5 to paying something which does not make us any better off.

Let’s Discuss the Prisoner’s dilemma: A Famous game theory Example

Prisoner’s dilemma is the best known game of strategy. It helps us to understand what monitors the balance between team work and competition. In the traditional version of the game, the cops have arrested two suspects P1 & P2 and interrogating them in separate rooms. The police don’t have enough evidence to convict them. If they could get a confession from either of them then they can convict them both. They have four options now:

If P1 confessed and P2 stayed silent then P1 would go free and P2 would be charged robbery for 10 years and of course this worked in other way to.

If P1 and P2 both confessed then they receive 8 years of jail. If both stayed silent then they would receive 1 year in prison.

The 2 prisoners left to make their decision without a way to associate each other. “What did they choose?

According to Nash Equilibrium the best solution for the two prisoners was to stay silent and get 1 year of prison. This prisoner’s dilemma very much exists in real life world like Companies competing against each other for money, Countries competing each other in war. Its most recent impact was seen in the Greece Crisis which has been used in studies of corruption and mutual development between Euro zone and Greece.

Read More :Understanding the Greek Crisis

Nash equilibrium and Greece crisis:

Greece had two main problems; An Overvalued currency and extreme debt. The simple link between these two reasons was that a cheaper currency would result to decline in economic growth alleviate the debt situation. Now Greece had similar options like Prisoner’s dilemma.

  1. Fail to repay loan and stay in the Euro
  2. Fail to repay and leave Euro
  3. Accept Referendum and Stay in Euro
  4. Accept Referendum and leave Euro

Greece choose the third option to accept referendum.

http://blog.bearing-consulting.com/2015/07/12/summer-reading-list-inspired-by-greece/

In simple terms, If Greece Defaults (Not able to repay loan) then they won’t get any payoff. If Greece accepts the referendum then it would ease its strict rules on fiscal policy and accept the loss on holdings of Greece debt. So overall payoff will be (1, 3/4)

If Euro zone rejects the deal, Greece would be unable to pay to its creditors and this would lead to a technical default. The first scenario (0, 0) is bad for everyone but the second scenario is pretty good for Euro zone (0, 1). Nash equilibrium applicable here and both Greece and Euro zone benefited here by accepting the third payoff option (1, 3/4).  This is becomes the best option for Greeks to accept similar to the prisoner’s dilemma both players avoided major crisis by mutual cooperation.

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