Stochastic signaling: information substitutes and complements

I develop a model of stochastic costly signaling in the presence of exogenous imperfect information, and study whether equilibrium signaling decreases ('information substitutes') or increases ('information complements') if the accuracy of exogenous information increases. A stochastic pure costly signaling model is shown to have a unique sequential equilibrium in which at least one type (and possibly all) engages in costly signaling. In the presence of exogenous information, a unique threshold level of prior beliefs generically exists which separates the cases of information complements and substitutes. More accurate exogenous information can induce a less informative signaling equilibrium, and can result in a lower expected accuracy of the uninformed party's equilibrium beliefs. An application to signaling in net- works, in which a social network is the source of exogenous in- formation, qualifies the relation between network characteristics (size, density, centrality, component size) and equilibrium signaling.