Countable Spaces and Common Priors
AbstractWe show that the no betting characterisation of the existence of common priors over finite type spaces extends only partially to improper priors in the countably infinite state space context: the existence of a common prior implies the absence of a bounded agreeable bet, and the absence of a common improper prior implies the existence of a bounded agreeable bet. However, a type space that lacks a common prior but has a common improper prior may or may not have a bounded agreeable bet. The iterated expectations characterisation of the existence of common priors extends almost as is, as a sufficient and necessary condition, from finite spaces to countable spaces, but fails to serve as a characterisation of common improper priors. As a side-benefit of the proofs here, we also obtain a constructive proof of the no betting characterisation in finite spaces.
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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp604.
Length: 35 pages
Date of creation: Apr 2012
Date of revision:
Publication status: forthcoming in IJGT
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