Prisoners of the Century – Game Theory and Prisoners
A game is generally a structured form of leisure, usually undertaken primarily for fun or entertainment, and occasionally used as a teaching tool. Games are very different from work, which often is conducted for remuneration, and even from fine art, which often is an expression of artistic or aesthetic values. Work is done for the sake of earning a living, while games are frequently undertaken as a way of escaping from reality and having a bit of fun. Games can be for single players, where the objective is to win the game, or they can be multi-player games, where a number of players compete against each other. There are many video game platforms currently on the market, each with their own unique style, personality, and offerings. It is up to the player to choose the platform that best matches his or her preferences and tastes.
Video game systems are typically designed around a number of fundamental theories. The most popular of these is called game theory. Game theory suggests that there are four important factors involved in a game’s design, and these include conflict, opportunity, balance, and consistency. Game theory applies to all four factors, but it is particularly important to understand how to successfully balance these factors, since this allows players to better participate in the game and, consequently, to enjoy it.
One of the most important concepts behind game theory is known as Nash equilibrium. Named after the great American mathematician John Nash, this concept states that the probability of an outcome being true, i.e. winning, is equal to the expected frequency of such an event taking place. For instance, if a pair of people walk down the street and have a chance of getting into a fight, each of them will strike the other one once, making the chances of them being able to do so again, or of any of them being able to strike at all, one, zero, or none, is exactly what the game theory says is likely to happen. To a certain extent, then, the prisoner game proves Nash equilibrium true.
However, the prisoner game also shows a weakness in the premises of game theory. Namely, it appears that the frequency with which people are able to strike each other, or fail to do so, is not constant throughout the game. For instance, a group of people can be expected to strike each other with a regular frequency up to a point, but for some individuals, the frequency of strikes might actually be lower than the frequency with which they can strike each other. To show this in a more formal setting, let us imagine two groups of people, A and B, who enter a room in the same physical location, with A and B each having twenty members. The size of the rooms does not matter; what matters is that they all share the same basic physical space.
Because of this, the value of each individual unit of currency drops slightly as the two players enter the room. Nash’s law then tells us that if we wish to assign a fixed value to the money of A and B, then the value of each units of currency for each player should equal their probability of striking each other. However, economic models based on the prisoner game theory suggest that if A and B are in a situation where they are confident they will not be attacked, then they will likely choose a non-prevalent strategy; therefore, their choices become more random, leading to a smaller drop in the value of units for each player.
The biggest problem with the prisoner game, as it turns out, is that it renders many of the important results of the game theory questionable. In particular, it renders the concept of monopoly rent-based competition problematic. Suppose, for instance, that we take our model Prisoner 1, a Prisoner 2, has an almost monopoly of goods, such that no one can produce any more of any kind (such as food or shelter) than he can. Then everyone in Prisoner 2’s neighborhood is forced into choosing the same kind of scarce commodity, leading to a severe reduction in the level of demand, leading to a rise in prices. Prisoner 2, however, chooses to deviate from the norm, buying more of whatever good he needs, causing the price to rise again.