The Beauty of Nash Equilibrium
John Nash, an American mathematician, was responsible for coining the famous ‘Nash Equilibrium’ that we’ve used at least once in our life. Yes, if you have played a game or been in a situation with more than one outcome, the theorem could have possibly be applied. For a situation that involved two or more players, Nash developed a strategy for each player such that the other would have no interest in changing his/her strategy regardless of what the other player was doing. This set of strategies is known as Nash equilibrium, one of the integral concepts in game theory and for which Nash received a Nobel prize.
In the article cited, it states that there is in fact a downfall of this theory. It doesn’t guarantee the best possible outcome for the players in the game; it suggests that the players are essentially ‘stuck’ in that no individual can change his/her outcome provided that they could not change the other individuals choices. On the contrary, I find some beauty to the madness as it proves one thing – that in any given situation, you either win or lose and both are certain. The individuals can either both have a positive or a negative outcome and the situation can also occur where one has a positive and the other has a negative result.
A famous example of the concept is the ‘Prisoner’s Dilemma’ shown in the playoff matrix below, when two persons are arrested for a some illegal act and are questioned independently of each other. There are several outcomes for each individual. If one suspect gives some evidence against the other, they get two years off of their sentence and if they are both suspected of a petty crime they will get two years of jail time. Consequently, if they are both suspected of a serious crime, this results in ten years on their sentences.
The outcomes go as follows; if suspect A talks and suspect B stays silent, then A will walk and B will get 10 years of jail time (and vice versa). If both A and B confess against each other, then they will both get 8 years, and if both stay silent then they will get 2 years of imprisonment. The Nash Equilibrium for this dilemma is if both suspects stay silent, where they will get two years of prison time each, while not optimal, these are the suspects best responses to each others choices.
There are so many more complex applications in which this theory could be applied which extends the measure of the true beauty of the concept. We have yet to see the next subject matter to which it will be applied…
http://theconversation.com/the-legacy-of-john-nash-and-his-equilibrium-theory-42343