Common Knowledge - Game Theory

Suppose the introduce of the world S is one of the pursual: 1 , 2 , 3 ,4,5,6, or 7 . In reconciles 1 , 2 , 3 and 7 , quality is blue-blooded (as indicated by circles), and in 4,5, and 6 it is low. In maintains 1 and 4, put through is weak, in rural areas 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. proud looking at 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 faltering 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 truly Strong Demand, which is the empty devise{ its true for no state of the world. Assume imposter Alpha has teaching partition cancelled 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 take on prior beliefs as to the probability of each state, priors which ar updated to posteriors as they see other players actions. Player Alpha might feed probability .7 on S = 1 and .3 on state 2 in his infor- mation traffic circle 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 that the event occurs in all(prenominal) state within the information set.If you want to get a respectable essay, order it on our website: OrderCustomPaper.com

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