Game Theory Games – Developing and Playing Your Own
A game is essentially a structured type of play, normally undertaken for fun or entertainment, and occasionally used as an educational resource. Games are quite different from work, which often is carried out simply for recreation, and from literature, which often is more of an expression of intellectual or artistic aspects. In work, one may be asked to carry out certain tasks in order to advance the objectives of the work. In games, one is never motivated by these requirements; indeed, many of the most interesting games involve trying to figure out how to beat a system, not to advance along a particular path. Often the object is not to win the game, but to explore the mechanics of the different strategies that a player can employ to gain the most advantage from the given situation.
The best game theory has to deal with the issue of spontaneous action. Spontaneous action occurs when two or more players decide to cooperate voluntarily and to choose to compete against each other rather than to obey the generally accepted rules. This leads to an increase in the rate of complexity, as players find themselves being forced into decisions that they would otherwise not have been able to take. The spontaneous nature of the game also increases its ecological validity: in a society where a majority of people are employed in jobs that demand sophisticated tools, it becomes much more important to make sure that these tools do not cause too much overall damage.
Games like Monopoly, Scrabble, and Risk are all examples of word games; those games involving property and finance, for example, require players to coordinate their borrowing and spending as well as their income taxation. The rules of Risk may prohibit players from investing too much money in certain areas, while the Monopoly board game may restrict the rent to the amount that the property may earn. The underlying principles of the game are important. Board games involving financial institutions or real estate may involve property dealings that the player must carefully consider. Some, like Scrabble, are purely luck-based; players may have a chance to gain valuable properties or buildings, but they may also choose to lose points or coins that they otherwise would have gained.
While the game mechanics may differ from the real world example, there is one similarity between board games and real world negotiations. In both cases, players must carefully choose how to interpret and implement the rules of the game. Some may prefer to treat rules as things that are completely independent from the game itself, allowing them to “go off the board” and ignore them; others, however, treat rules like constraints that must be adhered to, requiring players to follow them in order to play the game. Understanding these rules is important, as ignoring them can result in losing all the money and property accumulated during the game.
The Prisoner’s Dilemma is an especially well known version of the prisoner’s dilemma. In the classic formulation of this dilemma, a player is put in a cage with a set of three doors. Each door contains a hidden item; should the player open the door containing the item he or she desires, they are penalized with a two-point penalty. If they open the other two doors, they are rewarded with a three-point bonus. This is the most commonly used variation of the prisoner’s dilemma.
Nash equilibrium describes the idea that a game will settle into a steady, fixed rate of exchange, without the intervention of any outside forces. In the Prisoners’ Dilemma, for instance, the Prisoners are able to manipulate the rate at which they exchange points by selecting certain numbers. Without this initial exchange of information, the equilibrium cannot be reached. Using Nash equilibrium to explain the Prisoners’ Dilemma, players choose a number among their possible alternatives, keeping in mind the value of the extra point they will receive if they make that choice. With the help of a calculator, they then see if the equilibrium they established in the game theory tournament will hold in the real world.