Learning from Manipulable Signals

We study a dynamic stopping game between principal and an agent. The gradually learns about the agent's private type from noisy performance measure that can be manipulated by agent via costly hidden action. fully characterize unique Markov equilibrium of this game. find terminations/market crashes are often preceded spike in manipulation intensity (expected) performance. Moreover, due to endogenous signal manipulation, too much transparency inhibit learning harm principal. As players get arbitrarily patient, elicits no useful information observed signal. (JEL C73, D82, D83, G24, M13)