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Applicants of unknown types apply to multiple evaluators, seeking funding from one. Evaluators only want to fund High types, and see costless and private signals of applicants’ (i) types and (ii) rejection histories.
I study how evaluators’ equilibrium payoffs respond to (Blackwell) improvements in either signal. First, I characterise the effect of improving the type signal when the history signal is uninformative. This hinges on whether (i) the improvement is through stronger good news or bad news, (ii) adverse selection is relevant. I describe the decision rules maximising evaluators’ total payoffs, and the effect of improving type signals on payoffs when these are imposed.
Then, I show that a fully informative history signal maximises evaluators’ total payoffs irrespective of the type signal. Nonetheless, some Blackwell improvements of evaluators’ signals might reduce equilibrium payoffs.
