Consistent Beliefs without Common Prior

TL;DR

This paper extends Morris's characterization of common priors with full support to infinite type spaces, demonstrating robustness across different probability models and questioning the meaningfulness of a single common prior.

Contribution

It generalizes Morris's finite-type results to infinite spaces and shows the robustness of the characterization across belief models.

Findings

Characterization extended to infinite type spaces

Robustness across countably and purely additive probabilities

Challenges the meaningfulness of a single common prior

Abstract

In a strand of the literature, it is assumed that the common prior has full support; that is, every type of every player is assigned positive probability. Morris (1991,1994) established an epistemological-behavioral duality characterisation of the common prior with full support, showing that a finite type space admits such a prior if and only if it contains no acceptable bet. This result forms the basis of the present paper. The paper makes three contributions: (1) The characterisation of Morris (1991,Morris1994) is extended to infinite type spaces. (2) The extension is robust: it does not depend on whether the infinite model applies countably additive or purely additive probabilities as beliefs. (3) The analysis implies that the notion of a real common prior-understood as a single probability distribution or a set of probability distributions-is not necessarily meaningful.