Game Theory

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Game Theory:Main Article

Posted by chadbrochill on January 13, 2008

A normal game consists of a certain number of players and a set of moves, with that players have certain payoffs for a each combination of strategies. Most cooperative games are presented in the function form, while the extensive and the normal forms are used for non cooperative games.

Extensive form can be used to put games in an order of play, games are often presented as trees (picture to the bottom) The player is specified by a number listed by the vertex. The lines coming out of the vertex represent a possible action or move for that player. The payoffs or what the player gets in return for that move are specified at the bottom of the tree. Player 1 would choose either move U or move D, and depending on that the other player choose, either U or D depending on player 1’s move. These are the way basic non-cooperative games are played.

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 Player 2 chooses Left Player 2 chooses Right Player 1 chooses Up 4, 3 –1, –1 Player 1 chooses Down 0, 0 3, 4

The normal (or strategic form) game is usually represented by a matrix which shows the players, strategies, and payoffs (see the example to the right). In this example there are two platers. One of the players chooses 1 row and the other chooses the column. Along with this each player has strategies, which are showed be the number or rows and columns.  The payoffs are provided in the interior. The first number is the payoff that the first player gets (Player 1 in the example) The second is the payoff for the column player (Player 2 in the example).  As an example Player 1 plays Up and that Player 2 plays Left. Then Player 1 gets a payoff of 4, and Player 2 gets 3.

In cooperative games with “transferable utility” no individual payoffs are given because both players are working together for an equal goal. Instead, the characteristic function determines the payoff of each coalition. The standard assumption is that the empty coalition obtains a payoff of 0.

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Background

Posted by chadbrochill on January 13, 2008

The first known discussion of game theory occurred in a letter written by James Waldegrave in 1713. In this letter, he explained about how game theory could apply to the two-person version of the card game “le “Of course this was before and video games were invented, but it was still a very conceptual idea. Then in Augustin Cournot’s Researches into the Mathematical Principles of the Theory of Wealth in 1838 a general game theoretic analysis was pursued. Game theory boomed in the 1950’s, in this time many comcepts ofthe core, the extensive form game, fictitious play, repeated games, and the Shapley value were developed. Game Theory was then applied in political science and philosophy at this time. Then in the 1970’s Game Theory was then applied to many concepts of biology. This leads up to present day where Game Theory is used in many video games, to predict moves and concepts to approach situations in the right way.