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- W2107093521 abstract "This paper is a contribution to the study of the underlying mathematical structure of common-knowledge, which gives the well-known result of Aumann about the impossibility of ‘agreeing to disagree’. We present the Bayesian subjective probability model with player's belief: i.e. a triple (ℒ %plane1D;4AF;, μ), in which i is a player. ℒ is a lattice in the field of sets of a state space Ω, %plane1D;4AF;, is a correspondence assigning to each state ω a filter %plane1D;4AF;(ω) in ℒ, and μ is a common-prior. For this model, we impose none of the important restrictions on the information structure in the Aumann-Bacharach model: axiom of knowledge K1. axiom of transparency K2 and axiom of wisdom K3. We can extend both the disagreement theorem of Aumann and the agreement theorem of Geanacoplos and Polemarchakis under the assumption that each ℒ is an Artinian lattice." @default.
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- W2107093521 date "1997-05-01" @default.
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- W2107093521 title "Lattice structure of knowledge and agreeing to disagree" @default.
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- W2107093521 doi "https://doi.org/10.1016/s0304-4068(97)00785-4" @default.
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