In my opinion, CPA (Common Prior Assumption) is a part of a game structure.
This is in contradiction with Gödel’s Second Incompleteness Theorem, so we can’t state if the players are rational and intelligent or not, and if they know the game structure or not (with related loop “I know that you know…”).
That’s because I disagree with Aumann (1987): we need always an Harsanyi transformation, not only in case of incomplete information games. A player n+1 has to exist necessary, and we can call him God, State or Market. The most relevant issue is that he defines the game structure.
AUMANN (1987) Correlated Equilibrium as an Expression of Bayesian Rationality, in “Econometrica” vol. 55 http://www.econ.yale.edu/~dirkb/teach/pdf/a/aumann/1987-correlatedequilibrium.pdf
BOOLOS (1994) Gödel’s Second Incompleteness Theorem, in Mind vol. 103 http://www2.kenyon.edu/Depts/Math/Milnikel/boolos-godel.pdf
MORRIS (1995) The Common Prior Assumption in Economic Theory http://www.princeton.edu/~smorris/pdfs/paper_6_Common_Prior.pdf
Technische Universität Kaiserlautern – Harsanyi Transformation http://vwl-mikro.wiwi.uni-kl.de/fileadmin/user_upload/spieltheorie/0601.errata.s18to19and_39to40.pdf
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