Signaling with Performance and the Effect of Competition

Candidates compete to persuade a decision maker. The decision maker wishes toselect a candidate who possesses a certain ability. Then, as a signaling, each candidatedecides whether to perform a task whose performance statistically re‡ects the ability.However, since the cost of the performance is the same across all candidates, theperformance is a poor signaling device. This paper analyzes a "signaling game withperformance" in which the standard single crossing condition is violated. It is shownthat more competition makes the equilibrium signaling more informative when thelevel of competition is moderate. Moreover, the equilibrium signaling can perfectlyreveal the ability under a certain level of competition. On the other hand, too muchcompetition always makes the equilibrium signaling less informative.