Two Characterizations of Consistency
This paper offers two characterizations of the Kreps-Wilson concept of consistent beliefs. One is primarily of applied interest: beliefs are consistent iff they can be constructed by multiplying together vectors of monomials which induce the strategies. The other is primarily of conceptual interest: beliefs are consistent iff they can be induced by a "product dispersion" whose marginal dispersions induce the strategies (a "dispersion" is defined as a relative probability system, and a "product" dispersion is defined as a joint dispersion whose marginal dispersions are independent). Both these characterizations are derived with linear algebra.