Exists in probability theory a rule, called Bayes’ of attributing a priori probabilities to the occurrences of a random event, then review these probabilities by observing the outcome of an experiment on such an event, and finally revised probabilities are called a posteriori.
Now, in a game with incomplete information, inevitably presents the calculation of probabilities, in relation to the occurrence of various types, but also the possible reactions of the players which they are the expression. Such calculations are subjected to revision course, based on observed behavior: it takes the idea a priori Bayesian a posteriori probabilities. Is seen as an equilibrium will, in effect, to the extent that the idea of balance is inseparable from that of invariance that is “nothing moves” so that a balance needs to be consistency between the odds priori and a posteriori in such a way that players are not encouraged to revise their plans. A balance that has this property is called in game theory Bayesian equilibrium.
In this type of equilibrium beliefs of each, on how to react to the others play a decisive role, while observed by the players, are the behaviors of the “other” but not their actual rates. To set your plans, seek to estimate these rates on the basis of their probabilities of occurrence, as the idea that they are made, and what they believe is the way they react to the other according to whether this or that kind. Such beliefs usually take the form of a probability distribution: “If this work is of the” right “, I think there is an x% chance to work with dedication and 1-x% that do not”; “if it is awkward and% there is a chance to work with dedication and 1-y% do not. ” While we can not forget that players observe their behavior to deduce its type, and also may have an interest in pretending to others that are of a different type that are actually a clumsy worker working etc would go through. However, those watching should, quite rationally, to consider this matter and so on. It measures the complexity of the calculations and expectations resulting from a similar process. For this reason, game theorists are content to beliefs given, without specifying their origin or training too, thus a limit to the principle of rationality.
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