Too Cool for School? A Theory of Counter signaling

In sender-receiver games high-quality types can distinguish themselves from low-quality types by sending a costly signal. Allowing for additional, noisy information on sender types can radically alter sender behavior in such games. We examine equilibria where medium types separate themselves from low types by signaling, but high types then differentiate themselves from medium types by not signaling or counter-signaling. High types not only save the cost of signaling by relying on the additional information to stochastically separate themselves from low types, but in doing so they separate themselves from the signaling medium types. Hence they may countersignal even when signaling is a productive activity. To evaluate this theory we report on a two-cell experiment in which the unique Nash-equilibrium of one cell involves counter signaling by high types. Experimental results confirm that subjects can learn to countersignal.