Separating signaling equilibria under random relations between costs and attributes: discrete attributes

We identify conditions for separating signaling equilibria where attributes are randomly related to costs. Under discrete attributes, a necessary and sufficient condition is the ordering of the cost distributions conditional on attributes by the Monotone Likelihood Ratio Property (MLRP). An equivalent condition is the monotone ordering of the cost elasticities of these distributions. Under a continuum of attributes, a necessary and sufficient condition is ordering by the cost elasticity 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 a continuum of attributes, to the condition of ordering by the MLRP. We, thus, introduce the definition of Generalized MLRP which orders posterior distributions induced by distributions as well as by particular realizations. We examine a “Spence labor market” in which education costs are randomly related to productivity. JEL Classification Code: D82