BELIEF NON-EQUIVALENCE AND FINANCIAL TRADE: A COMMENT ON A RESULT BY ARAUJO AND SANDRONI

Aloisio Araujo and Alvaro Sandroni have shown in [1] that in a complete-markets economy in which there are no exogenous bounds to financial trade, existence of equilibrium requires agents with prior beliefs that agree on zero-probability events, and, therefore, with asymptotically homogeneous posteriors. This note illustrates the extent to which the result depends on market completeness: in general, equilibrium requires compatibility of beliefs only up to the revenue transfer opportunities allowed by the market; when the market is sufficiently incomplete, generically on the space of asset returns, even individuals who disagree on zero-probability events meet that constrained-compatibility" requirement."