In memory of John Nash - legendary economist
JOHN FORBES Nash Jr, winner of the Nobel Prize in Economics in 1994, died in a car crash last Saturday. Nash won the Nobel Prize following the significant impact of his innovative work in game theory over the last 50 years.
Nash, a schizophrenic mathematician/economist, pioneered the 'Nash equilibrium' in game theory, which revolutionised the way individual economic agents approach and negotiate with each other to get the best outcome, regardless of what the others do. Nash's life inspired a book and a movie, A Beautiful Mind, which helped to popularise game theory.
What is game
Game theory is the part of mathematical economics designed to analyse strategies for dealing with competitive
situations. Firms apply game theory strategies in corporate mergers and acquisitions, etc. Government and the military apply game theory strategies in geopolitical diplomatic negotiations for war, or trade, or otherwise. Game theory is also applied in space science, engineering, stock market and international business. It has many different fields, including, but not limited to, cooperative games, non-cooperative games and strategic games.
How did Nash coin the concept of the equilibrium?
Nash thought of the concept when he and three of his friends were negotiating how to approach a group of women who were making eye contact with them in a bar. One of the girls being 'hotter' than the other four, Nash's friends recommended that every man should pursue her only. Every man for himself, may the best man win, in the pursuit of self-interest as recommended by Adam Smith's approach to economics.
Nash objected, indicating that such an approach was flawed. In this case, competition between them would become too overwhelming. The girl would end up choosing none of them, and no one would 'get laid', which is the worst possible outcome. He recommended instead, that they should all pursue the friends who were not so hot, show them attention and each man would be in a better position to 'get laid'. Operating in the interest of the group supersedes operating in self-interest, leading to a better outcome.
What is the Nash Equilibrium?
Basically, interactions between persons, firms and/or government can be broken down into games, where each player has more than one choice of action, leading to the possibility of different outcomes. Here, the outcome of a particular choice of action depends critically on the choice of actions of the other players. Each player examines the possible actions of the other players, match it with their own actions and attempt to predict the likelihood of each possible outcome.
The aim is for each player to select his strategy that produces the best results, irrespective of the action of the other player(s). The outcome from such actions is referred to the Nash equilibrium and is the best solution to the game. The Nash equilibrium is widely explained using the prisoner's dilemma, where individuals acting in self-interest pursue a course of action that does not lead to the best possible outcome. One should instead pursue the interest of the group to achieve the best possible outcome, or achieve a Nash equilibrium.
What is the prisoner's dilemma?
Imagine a situation where the police arrest two suspects to a crime and are interrogating them in two separate rooms. Each has two choices, confess, thereby implicating the other, or deny the crime. The police tell each of them that if they confess, they will serve a shorter sentence, but if one denies and the other confesses, the person who denies will serve a longer sentence. No matter what the other person does, each can improve their situation by confessing.
In this case, the optimal thing to do is to confess, assuming that the other suspect confesses, a confession will produce a shorter sentence. But if both confess, the outcome is worse than if both deny the act. So even though confession would be the 'dominant strategy', denying would produce the best outcome.
- Dr Andre Haughton is a lecturer in the Department of Economics on the Mona campus of the University of the West Indies. Follow him on twitter @DrAndreHaughton; or email email@example.com.