So far, we have assumed that information was complete, and each player knew all outputs and potential profits, but also knows everything about others, including their behavior. Moreover, even under this scenario extremely strong, clear results are obtained and defined.
However, despite this, the assumption of complete information, an impediment to distinguish situations particularly interested in the micro-economists, such as those mentioned at the end of the previous chapter, concerning the relationship between principal and agent. The need to alleviate this hypothesis is felt more and more.
Now, it is clear that if there are “too many” gaps at the level of information available, players can not make a reasonable choice, given the limited basis of calculation that have or at least for a systematic mathematical treatment. For this reason, game theorists have attempted to introduce into their models limited dose of uncertainty, in order to preserve capital theory – proceeding, representations, concepts – the full information approach.
The use of fictitious play: Nature.
Games with incomplete information are generally presented as follows: players are supposed to be a “type” or other (eg business or awkward or even “low cost” or “high costs”). So, everyone knows its exact type, but only the set of possible types of the others, it appears the need to assign a probability of occurrence to each of the different types. It is because of ignorance on the part of players – or some of them – the type of the other – or some of them – where lies the inadequacy of information, such failure is, however, limited, as is assumed that solutions and profits are known to all, regardless of possible eventualities, ie, whatever the forms taken by the various types of players.
Game theorists formally introduced in their models a fictional character called Nature and whose only “activity” is to attribute a type to each of the players, with a certain probability. So that a game with incomplete information appears as a complete information on which confront all the guys who are players in a game which expanded and Nature intervenes first. In this way a game with two participants, which may have three to one and two for two, will have 3 * 2 = 6 boards that represent potential gains, according to the strategies chosen, in a game with complete information there is only one board. This suggests the complexity of the calculations necessary to determine optimal strategies.
Possibility Related Games:
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