Publication Date: May 2000
We consider a principal who is keen to induce his agents to work at their maximal eﬀort levels. To this end, he samples n days at random out of the T days on which they work, and awards a prize of B dollars to the most productive agent. The principal’s policy (B,n) induces a strategic game Γ(B,n) between the agents. We show that to implement maximal eﬀort levels weakly (or, strongly) as a strategic equilibrium (or, as dominant strategies) in Γ(B,n), at the least cost B to himself, the principal must choose a small sample size n. Thus less scrutiny by the principal induces more eﬀort from the agents.
The need for reduced scrutiny becomes more pronounced when agents have information of the history of past plays in the game. There is an inverse relation between information and optimal sample size. As agents acquire more information (about each other), the principal — so to speak — must “undo” this by reducing his information (about them) and choosing the sample size n even smaller.
competitive prizes, extensive form games, information patterns, strategic equilibria, optimal sample sizes
JEL Classification Codes: C720, D820, J410
Published in Journal of Mathematical Economics (December 2001), 36(4): 311-336 [DOI]