Separating signaling equilibria under random relations between costs and attributes: Continuum of attributes

We identify conditions for separating signaling equilibria where costs and attributes are randomly related and where both take a continuum of values. A necessary and sufficient condition is the ordering by the cost elasticities of the cost density functions with respect to the original probability measure and with respect to a probability measure modified by the "attribute payoff function". This condition is the equivalent, under the continuum of attributes, to the condition, under discrete attributes, of ordering by the Monotone Likelihood Ratio Property (MLRP) that Feldman (Mathematical Social Sciences, 2004, in press) found in a companion paper. We, thus, introduce the concept of generalized MLRP (GMLRP). While the original MLRP ranks only posterior distributions induced by particular realizations, the GMLRP ranks posterior distributions induced by distributions as well.