Monday, March 23, 2015

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Fundamental laws of game theory:

Game theory is used for analyzing how individual agents interact with each other. Depending on the structure, they may take into account how the other agents are choosing (or how they believe that they will choose), and then decide on their own strategy. This closely resembles the situation in many parlor games. Think, for instance, how the players act in chess: They only decide on their own moves, but they do so depending on how they believe that the opponent will respond. It is most often a bad strategy to hope that the opponent will not discover a trap. A better strategy is to assume that the opponent learn several thing that one understands oneself, and then base one’s policy on that.

To revolve this into a theory, we need to first define the basic building blocks. For a game to be a game in the applicable sense, we need players, regulations, outcomes, and preferences over the outcomes. By means of chess, the players are “white” and “black,” the rules are the rules for chess, the common outcomes are “white takes black’s king,” “black takes white’s king” or “draw.” The players’ preferences are usually that they have a preference that they take the opponent’s king to a draw, and lastly that the opponent takes their king. In most games of game theory, we need to specify:

·         The players. It could be persons, firms, or countries. Frequently, there are only two or three players.
·         Actions. All achievable actions the different players can choose to do, for instance decide on quantity or price.
·         Information. What each player knows at dissimilar stages of the game.
·         Strategies. A policy is a complete description of what a player will choose at every possible situation that could arise in a game. One can think of a policy as a list. The list should be so comprehensive that player, and never actually have to decide anything by herself.
·         Payoffs. The usefulness a player gets, given a certain outcome of the game.

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