Game Theory it's nothing but a way of understanding people choices while "playing a game". More generally understanding as Game any situation where one or several "agents" took action, being this agents the players. In game theory the main analysis is set on the "strategies" that are nothing but the players choices.
Games are usually divided into Cooperative and Non Cooperative, referring to players cooperation, chess would be a classic example of a Non Cooperative one because both players are of contrary sides while monopoly could be Cooperative anytime people decided to help each other to defeat the rest of the players having more tosses of the dice, money and properties.
Another classification that it's usually taken into account it's refers to the Information the players have while playing. Another basic definitions are:
Dominant Strategy: a strategy it's said to dominate another if and only if disregarding the other players choices the use of this strategy give him better payoffs. Therefore a strategy it's said to be dominated if exists a strategy that dominate it.
Payoff: Players are suppose to receive a either positive or negative payoff in any position of the game. a payoff it's a number that reflects the desirebility or not of a strategy according to the other player ones
Rationality: A player it's said to be rational if he plays with the objetive of maxime his payoffs.
Zero Sum Games: An n players game it's said to be a zero sum if in each play the sum of the players payoffs it's zero, in a two player game that would lead to two opposite players, their payoffs are always the same in magnitude but of different signs.
Nash Equilibria: It's a list of strategies, one for each player with the property that non player can change his own strategy and receive a better payoff.
Finite Game: A game it's said to be finite if every player have a finite number of strategies.
Non Cooperative Games are described in two classic ways:
Strategical or Normal Form and the Extensive Form. In the Normal one the game it's described by a triplet of two sets and an order relation:
J : the set of all players
Si : the set of strategies for the i player
>i : preference relations asociated to each player(a,b belongs to Si, a it's prefered to b if and only if a>b ). And the game it's printed in a payoff matrix that reflects the payoffs every player receive. For example there's a classic game called the Prisoner Dilemma, where two suspects are arrested without proofs and they are interrogated if they both cooperate and declare themselves guilty they receive a payoff 6, if one of them cooperate and the other one defect they receive 0 and 9 respectively while defecting give them a payoff 1. Here the payoffs are referred as months in prison, so the wise rational desition would be to minimize their's payoff. An strategical representation of this game would be:
While in the Extensive form the Game it's represented as a Tree Game. Every position of the game it's put as node of the tree. This is to give a better idea of a time-depending game because it focus on all the possible desitions to be taken and all the possible responses to it making explicit the time.
This it's nothing but a too brief description of game theory, that could be really useful for game developers by giving you algorithms for achieving Nash Equilibria, so if anyone feels interested for Game Theory I have many really good papers on GT. I'm particullarly interested in applying Genetic Algos to solve Games. If there's either anyone interested on GT who wants me to help him/her or if anyone to help me with the Genetic Algorithms-Game Theory connection that I need I will gladfully answer :excl: /thank for it!!!!!!!!