Sunday, 2 November 2014

John Nash: Game Theory and the Equilibrium

By Calvin Price

In 1950, John Forbes Nash Jr. earned a doctorate for his work on game theory.  His dissertation focused on what players do in non-cooperative strategic games.  Since his original work, game theory has been hailed as one of the greatest intellectual advances in economics and has had applications on a vast range of fields.  It was truly a worthy cause for Nash to win the Nobel Prize in 1994.

Game theory can be summed up in a disarmingly simple question: what will the other guy do?  It focuses on what a person will do when confronted with the move of another person.  This is called game theory because that’s where it can be most obviously applied.  While it’s unnecessary in games such as rock-paper-scissors or tic-tac-toe, game theory becomes much more useful for something like chess.  This has clear implications as a mental construct for thinking about complex games, but it otherwise seems like an exercise in mathematical thinking.  What about real-life situations?

The most famous of game theory applications is called the prisoners’ dilemma:
Two men have been arrested.  The police have them on minor charges, but suspect a larger crime.  If they get the testimony from one of the men, he will be freed and the other will be locked up for 10 years.  If neither man betrays the other, they both get 1 year imprisonment.  If both men talk, then they each get 5 years.

So, what do you do?