Characterizing Common Priors in the Form of Posteriors

From posteriors to priors via cycles: An addendum

“…1 The algebraic approach provides an alternative to the syntactic approach of [1], as well as the semantic approaches that are based on separation theorems ( [3], [6]) or on limits of iterated expectations in Markov chains ([5]). In a model with finitely many players and a finite state space, the algebraic approach requires the verification that the posteriors satisfy a given set of equations, the so-called cycle equations.…”

Speculative trade under unawareness: the infinite case

“…For instance, it might prepare for other versions of the "no-speculative-trade" results, where the positivity assumption is dropped (and hence any player could have uncountably many types). Feinberg (2000) and Heifetz (2006) prove results on the absence of common certainty of speculative-trade in some states without the positivity assumption. We focus on the absence of common certainty of speculative-trade in all states.…”

Agreeing to agree and Dutch books

“…Indeed, if P is a common prior of (t i ) i∈N , then define t 0 = P . Then all the agents in N ∪ {0} have a common prior and an agreeable bet which is impossible (see Morris, 1994;Samet, 1998, andFeinberg, 2000).…”