Stochastic signaling: information substitutes and complements

In a model of stochastic costly signaling in the presence of exogenous imperfect information, I study whether equilibrium signaling decreases (‘information substitutes’) or increases (‘in- formation complements’) if the accuracy of exogenous informa- tion increases. A unique threshold level of prior beliefs generically exists that 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.