Persuasion and learning by countersignaling

We model countersignaling (i.e., very high types refraining from signaling) arising from the tradeoff between persuasion and learning in a signaling game. We assume that the agent has imperfect private information regarding his/her productivity, which the signaling action provides additional verifiable information about. A higher-type agent benefits more from providing such objective, albeit imprecise, "proof" for the market, but may also gain less from learning about his/her productivity. When the latter effect dominates the former for the very high types, the equilibrium exhibits countersignaling: very high and low types pool on refraining from signaling, and only the medium types signal. Under certain conditions, the countersignaling equilibrium is the unique pure-strategy perfect sequential equilibrium.