Principal-Agent Models Where a Principal is only Affected by Extreme Performances

In multi-agent settings, the principal can reward agents according to their rank-order achievements, or by their absolute achievements. On the other hand, the principal may be affected by the sum of the agents' achievements or by only the highest or lowest achievement. We consider absolute rewards where the principal is only affected by the highest or lowest achievement. The scenario of highest achievement corresponds to, for example, parallel R&D teams, where only the highest/best achievement matters. The scenario of lowest achievement corresponds to, for example, an assembly system, where the number of component sets available is the minimum of the components' quantities. The principal is assumed not to know the agent's type in terms of its noise distribution, so he faces “ambiguity”. We derive the optimal value of a key parameter of the reward function and compare its values for different objectives. When extreme performances matter we find that a principal will employ weaker incentives for multiple agents and that the reward parameter is even smaller if only the lowest achievement is relevant. We mostly assume multiplicative uncertainty, but also address additive one. We then consider an ordinal-cardinal model