What is the Nash Equation?

A game is generally a structured type of play, normally undertaken for fun or entertainment, and occasionally used as a teaching tool. Games are very different from work, which typically is done for pay, and from literature, which is basically an expression of aesthetic or political values. In the former cases, the point of the game is to pass the time, the latter to learn something. With regard to learning, games are the one of the simplest ways to teach people important concepts through simulation, through strategy and through imitation. As regards strategy, board games, word games and puzzles are among the most common approaches.

Nash equilibrium is, perhaps, the most famous game theory that applies to all economic games. The game theory states that there is such thing as gain and loss in all economic transactions. Gain is what we make when we acquire something from lending or borrowing, while loss is what we have to suffer when we give up the same object or service to someone else. Nash equilibrium states that all these losses and gains should be equally shared by the parties involved in the transaction, in the same proportion as their proportion in the scale of values of the things they are giving and receiving. Otherwise, the equilibrium is upset, leading to the institution of monopoly or concentration of wealth, monopoly or concentration of profits.

The prisoner’s dilemma is another important application of game theory. The prisoner’s dilemma is based on the idea that two players, A and B, have unique expectations and desires from a game. Prisoners, being of the essence of a zero sum game, have exactly the same number of possibilities as the number of possible outcomes, while also having the same particular number of possible results. For example, if one player is at a ten chance of getting the highest score, then he is said to be ‘off balance’ and will share with the other player, who is at a ninety percent chance of getting the lowest score. This can be illustrated with the classic ‘prisoner’s Dilemma’. In this instance, it is not the outcome that is relevant, rather the balance of interest that is between the two players.

The prisoner’s dilemma is also applicable in the dictator game, where a single leader has the potential to dominate a given population. If the leader uses his/her resources to collate information that will help him/her get ahead, then this can lead to the domination of the population by this leader. The same applies if the leader decides to’sell out’, i.e. to make goods in the market that are in high demand to the mass majority, thereby putting the minority on the brink of starvation.

In the latter instance, the dilemma of the prisoners’ dilemma also applies to the dictator game. If a group of people are put in a situation where they have nothing to lose, but a great deal of value to gain, then they will usually opt to defect and help the majority to win. This scenario applies to defections from amongst military personnel who may be put under surveillance. Similarly, it may also apply to groups of terrorists who may decide to blow a terrorist cell in order to protect their own lives.

In the end, both games have something to do with the Nash equilibrium, which refers to the fair mean number of points that will always result from any game analysis or game play. Nash’s famous statement – that one man, one vote and the same probability for each of the players – is obviously true in all but the purest of games. However, it does mean that the Prisoners’ Dilemma and the dictator game, whilst being symmetrical, are not the same game. When both players know that they are up against information of the other, and are not bluffing, then they are using the same information to select their moves.