Common Knowledge - Game Theory

Suppose the introduce of the world S is one of the pursuance: 1 , 2 , 3 ,4,5,6,
or 7 . In reconciles 1 , 2 , 3 and 7 , quality is gamy (as indicated by circles),
and in 4,5, and 6 it is low. In maintains 1 and 4, consume is weak, in states 2
and 5 it is medium, in states 3 and 6 it is strong, and in state 7 it is very
strong. Well focus on quality in these notes.
An point is a particular characteristic of zero, one, or to a greater extent states.
High tone of voice is the event we will study, denoted by E. An analogous to
High Quality is that S 2 f 1 2 3 7 g: another(prenominal) event is Weak Demand,
which says that S 2 f 1 4g: Another event is Weak Demand and High
Quality, which says that S 2 f 1 g: Another event is Low Quality and Very
Strong Demand, which is the empty devise{ its true for no state of the world.
Assume Player Alpha has teaching partition off
f 1 2 g f 3 4g f5 6 7 g
That means that, for example, if the state is 1 , he can strike that the
state is either 1 or 2 , yet not which of those.




Assume Player Beta has information partition:
f 1 3 g f 2 4g f5 6 7 g
Assume Player Gamma has the information partition:
f 1 g f 2 g f 3 g f4g f5 6 7 g
The players have prior beliefs as to the probability of each state, priors
which ar updated to posteriors as they see other players actions. Player
Alpha might dedicate probability .7 on S = 1 and .3 on state 2 in his infor-
mation set f 1 2 g, for example. He might put probabilities of 1.0 and 0.0
on the elements of his information set f 3 4g.
Denition: Player Alpha knows X if he observes an information set such
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