Bayes And Game Theories

Bayes’ theorem is the result given by a conditional and marginal probability distribution of a random variable.

Game theory uses models to study interactions in structures of formalized incentives (called games). It studies the election of the best conduct when the costs and benefits of each option are not fixed in advanced but they depend on the election of the other players.

There is a specific game case: the incomplete information game. It is when the players do not know all the characteristics of the game. These unknown parameters are called types. The players who have not complete information have to maximize the expected value of their types once the distribution of the other players’ types is given. They have to maximize this expected value because they can not calculate it with precision since they don’t know some information about the game.

Bayes’ theory tries to solve these incomplete information games turning it into imperfect information ones. This imperfect information is given by probability. Bayes thinks that the most important thing is prior knowledge, so in his theory the players of the game are supposed to act with conditional strategies. They have to consider the possible actions of the other players and using probability methods, they can construct a knowledge about the game.

The equilibrium which is tried to be reached is a pair directed by a combination of strategies and a belief system. The beliefs are probabilities assigned to each node in a set of information. The player assigns probabilities to the occurrences of each node. That is how the players can make decisions among the different options that are in the game.

As far as I am concerned Bayesian theory is related to Game theory because it gives to the players the opportunity to select the best option for them in the case of incomplete information games. The Bayesian theorem