Tournaments with gaps

•We analyze a moral-hazard problem with two risk averse agents.•Since performance is unverifiable a tournament is used as a credible incentive scheme.•Standard tournament contracts specify only tournament prizes.•We show how this standard tournament can be modified to reduce labor costs.•Such reduction is possible under unlimited liability but not under limited liability.

A standard tournament contract specifies only tournament prizes. If agents' performance is measured on a cardinal scale, the principal can complement the tournament contract by a gap which defines the minimum distance by which the best performing agent must beat the second best to receive the winner prize. We analyze a tournament with two risk averse agents. Under unlimited liability, the principal strictly benefits from a gap by partially insuring the agents and thereby reducing labor costs. If the agents are protected by limited liability, the principal sticks to the standard tournament.