Its all about the GAME!!!

Jon Forbes Nash Jr....The name reminds us of Oscar winner Hollywood blockbuster "A beautiful mind" and to an extent superb role play by Russle Crowe, but what we often forget is the true picture of schizophrenic and his popular “Game theory” which has its application spanning across economics, biology, politics and philosophy. When I finished reading the life history of Sir John Nash, I was tempted toward Game theory the aspect which remained largely untouched in the movie.
It is the concept used in the strategy based game where the outcomes are known to all the players and they play in actual conditions to maximize their chances of winning the game often forgetting that the most mutually favorable outcome is not the beneficial to both(or all) the players individually. Lets take most popular “prisoner dilemma” problem and try to illustrate the solution

“Police have detained two criminals accomplice in a grave crime. But due to lack of evidence the personals decide to question each of them individually. The options with both the prisoners are to either accuse or not to divulge any details. The matrix below shows the possibilities and the outcomes

both the prisoners together serve minimum imprisonment of an year when they remain silient which is highly enlikely since if the other betrays then the law hit the silent prisoner hard.

one more example to illustrate the "Game Theory" is the "The ultimatum game" in which the sample space of the possible outcomes is infinite as aginst the one given above with sample space as 4 possible outcomes. This game involves dividing the share onto two parts with the the first gamer given the option of choosing the share fot both of them and the other given the liberty to reject knowing that both will not be given any share if it leads to rejection. Here the outcome favourable to both of them is that the second player accepts whatever is offered since(other than a zero) the desicion to reject will leave nothing to their disposal.

When a study is incorporated amonsgst many games played then a 50:50 share is most favourable amongst the players since all the other outcomes invauriably are more favourable to the first player dividing the share since he will keep his share to be more or equal to the second player.

the extensive representation of the conditions are shown as tree diagram as against the normal diagram shown for the "prisoners dillema" game above.

The MRI scan of the brain of second player in the study dipicts that the rejection is more often the result of revenge which is disastrous to both the player.

Studying these two games brings out a very interesting fact, in almost all the games played the most favourable outcome to all the player is often not the final outcome since it involves the rational thinking of maximizing the overall outcomes rather than the involving maximizing the indivisual outcomes.

This is one form of game theory in which the opponent is known. The other being rather unconventional in which the theory becomes complex in finding the outcomes.