So what is Nash Equilibrium?

The central character of A Beautiful Mind is a mathematician / economist by the name of John Nash, who is most famous for his theory of Nash equilibrium. The basic concept of Nash equilibrium is that in sequential game theory you should work back from the end of the game, in order to determine the best decision to make at the beginning of the game. In the movie this is explained briefly by means of a situation in a bar where there are four guys and five girls - one of whom, the blonde, is regarded as the ideal woman. In any of the guys choose to go after the ideal woman, the remaining four women will take themselves out of the game, and thus at most only one of the guys will be satisfied (albeit with a major 'score'). The better option is for each of the guys to go after one of the less desirable women. That way each guys succeeds in obtaining a mate. The only loser in this particular Nash equilibrium is the ideal woman, but the problem is defined in terms of the outcome the four guys acheive as a group.

All of this is particularly relevant to my current study at b-school. This Friday we're sitting our mid-term exam for Managerial Economics. One of the most popular problems that we've been working on during our study time is a Nash equilibrium problem concerning five executives and 100 golds coins. Here's your chance to experience the study life of an MBA. Post your answers in the comments to this blog entry (current MBS students please stay out of the 'game').

Five senior executives (A, B, C, D, E) are on a diving expedition when they find 100 gold coins. There exists a hierarchy amongst the executives such that A is the most senior and E is the least. Moreover, A proposes a division of the 100 coins and that is voted on. If the proposed decision is voted down (i.e. a majority vote against the division), then A is thrown off the ship and the next most senior executive, B, proposes a division of the 100 coins. As before, if this is voted down (a tied vote results in the division being accepted), B is thrown off the ship, and C is left to propose the division. And so forth. Assuming that all the executives are rational, what offer will A make to the executive team?

(problem adapted from an original Melbourne Business School question)