Common knowledge: the case of linear regression

Article Abstract:

The multivariate McKelvey-Page theorem is reinterpreted as a special case of a result regarding orthogonal projections in a Hilbert space. If the distribution of signals and payoffs were elliptical and that linear signals provide the information, the McKelvey-Page theorem is reinterpreted as a result about matrix algebra. When applied to Grossman's securities market model version, it was shown that the equilibrium price is common knowledge only if all investors agree on their conditional expectations of payoffs, This suggests that the linear rational expectations equilibrium is unique.

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On rational preferences

Article Abstract:

The close correlation between logical chains and rational preference orders offers a mechanism through which rational preference orders can be analyzed. The link can be successfully utilized in fulfilling partial information and in ascertaining a preference base's rational closure. Moreover, all undisclosed preferences can be discovered through the association. These conclusions assume the existence of a logically finite fundamental language and assume no random propositional language analog.

Economics, Research and Development in the Social Sciences and Humanities, Economic aspects, Mathematical logic, Symbolic and mathematical logic

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