Signaling with performance and the effect of competition

Candidates compete to persuade a decision maker. The decision maker wishes to select a candidate who possesses a certain ability. Then, as a signaling, each candidate decides whether to perform a task whose performance statistically reflects the ability. However, since the cost of the performance is the same across all candidates, the performance is a poor signaling device. This paper analyzes a 'signaling game with performance' in which the standard single crossing condition is violated. It is shown that more competition makes the equilibrium signaling more informative when the level of competition is moderate. Moreover, the equilibrium signaling can perfectly reveal the ability under a certain level of competition. On the other hand, too much competition always makes the equilibrium signaling less informative.