On 23rd May, 2015, one of the greatest minds of the current times succumbed to death in a car accident. John Forbes Nash Jr . - the great mathematician.
His theories in Game Theory, Partial Differential Equations, real algebraic eqautions and differential Equations have revolutionalized the world of Mathematics, Economics , Accounting, Computer Science and yes - Philosophy !
he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi. In 2015, he was awarded the Abel Prize for his work on nonlinear partial differential equations.
In 1959, Nash began showing clear signs of mental illness, and spent several years at psychiatric hospitals being treated for paranoid schizophrenia. After 1970, his condition slowly improved, allowing him to return to academic work by the mid-1980s. His struggles with his illness and his recovery became the basis for Sylvia Nasar's biography, A Beautiful Mind, as well as a film of the same name starring Russell Crowe,
I find his concept of Nash Equilibrium and the application of Game Theory in Prisoner's Dilemma very fascinating and in this post, I will elaborate on these.
Nash Equilibrium, stated simply goes like this.
Anita and Sunita are in Nash equilibrium if Anita is making the best decision she can, taking into account Sunita's decision while Sunita's decision remains unchanged, and Sunita is making the best decision he can, taking into account Anita's decision while Anita's decision remains unchanged.
tated like this, this theory of Strategic decision making , made me feel that isn't this how we all come to decisions ? We do it instinctively , with our years of wisdom and experience. But think about the situation, where we do NOT have enough experience and hence no instinct at all ... in that case, this mathematical approach helps us strategise and formulate the best decision to be taken. There lies the greatness.
Prisoner's Dilemma is another very interesting concept of Competitive Decision making derived from the Game Theory. I will explain with the following example :
Tanu and Manu have been arrested for robbing the Namo Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice.
A clever prosecutor makes the following offer to each.
He said : You may choose to confess or remain silent.
- If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice gets 20 years in jail
- Likewise, if your accomplice confesses while you remain silent, they will go free while you will be locked in the prison for 20 years.
- If you both confess I get two convictions, but I'll see to it that you both get early parole and get discharged within 8 years.
- If you both remain silent, I'll have to settle for token sentences on firearms possession charges and you will be released in 6 months.
If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.”
Here we see that the outcome of an individual is dependent on the decision taken by the other person !
The prisoners’ dilemma has applications to economics and business.
Consider two firms, say Coca-Cola and Pepsi, selling similar products. Each must decide on a pricing strategy. They best exploit their joint market power when both charge a high price; each makes a profit of ten million dollars per month. If one sets a competitive low price, it wins a lot of customers away from the rival. Suppose its profit rises to twelve million dollars, and that of the rival falls to seven million. If both set low prices, the profit of each is nine million dollars.
Here, the low-price strategy is akin to the prisoner’s confession, and the high-price akin to keeping silent. Call the former cheating, and the latter cooperation. Then cheating is each firm’s dominant strategy, but the result when both to “cheat” is worse for each than that of both cooperating.
In our day to day working too we have take decisions .
And maybe, instinctively, we follow the Game Theory. As explained in the above examples, we see that when both "Cheat" or both are "against" each other, the result of the decision is worse that if we considered the welfare of the others.