Head starts in dynamic tournaments?

•We study head starts in dynamic two-player tournaments a la Lazear and Rosen (1981).•A principal values aggregate effort and the highest effort exerted by the players.•It is always optimal to bias the tournament by awarding a head start.•A small head start increases the highest effort without decreasing aggregate effort.

In promotion contests or other tournament-like situations, a principal may attach some value to the highest effort expended by an agent. We show that whenever agents interact over multiple periods, awarding a head start to one of them is optimal even with completely symmetric agents. Awarding a small head start increases maximum individual effort without decreasing aggregate effort.