My interest in game theory begun when I stumbled onto Cristos Z. Konstas's website, author of one of the first textbooks on Psychohistory. Further reading on this subject seemed to indicate most efforts had some form of game theoretic framework (see Mechanics of History). So after a great deal of research and careful course selection, I was able to take a course on Game Theory at the Faculty of Economy.
Game theory is a branch of mathematics that analyzes the interaction between different rational elements subject to a given set of rules.
There three elements to a game:
Players are elements within the game. All players must make their payoff increase (or cost decrease). However the actions of each player affects the conditions of the game, thereby affecting other players. When all players have effectively obtained the maximum benefit possible, an equilibrium is reached and the game is concluded.
Strategies are the different behavioral alternatives players have. For example in a coin toss the player has two strategies, one for each side of the coin (supposing he can actually chose one of the sides). Each strategy is comprised of a payoff function (or cost function), that is the retribution obtained from choosing such a strategy. However as explained before each choice a player makes affects other players, so a certain strategy may only be good if other players behave in a certain way (hence the term function, payoff depends on other players strategies). Hence knowledge of other players strategies, and their payoff is key to the capacity for maximizing a game's payoff.
Strategies may have a fixed value and be absolute (for example going right instead of left on a race track). But they may also have a statistical nature and be mixed (for example throwing a die before the race and going right if the outcome is 2 and 4). Mixed strategies offer equilibrium for games that would not have an equilibrium otherwise.
These are limitations on the interaction of players, such as the number of cards on a game of poker or the number of players. Rules may be fixed, or change over time in which case the game is called an evolutionary game.
The number of turns is a very important rule. When only one turn is used, the game is called a static game. All players will chose an immediately favorable outcome. When many turns are used, the game is called dynamic. Dynamic games take into account the future interactions between players. Dynamic games may be finite or infinite. Finite games eventually lead to a static game and are often solved backwards from the last turn.
Its relevance to engineering has been studied only recently, and now is used for resource distribution, and intelligent module interactions among others.
Game theoretic framework coupling of two image segmentation algorithms.
