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

We identify conditions for separating signaling equilibria where discrete attributes are randomly related to a continuum of costs. A necessary condition is the ordering of the cost distributions conditional on attributes by first order stochastic dominance. A necessary and sufficient condition is the ordering of the cost distributions conditional on attributes by the monotone likelihood ratio property. An equivalent necessary and sufficient condition is the monotone ordering of the cost elasticities of these distributions.