Incentives design under parametric uncertainty

This paper investigates incentives design problems where the leader lacks precise knowledge on a certain parameter, which describes the problem situation, but the leader can collect information from the follower. We first illustrate that the follower may misrepresent information when the leader's strategy depends on information provided by the follower, To deal with incentives design problems in such a situation, two ideas are proposed, One idea suggests using a misrepresentation-proof optimal incentive strategy (MOIS), which can induce the follower to report true information and simultaneously to take actions in favor of the leader's interest; while the other idea suggests imposing threat to enforce the follower to reveal truth through using a mixed investigation strategy, Furthermore, in the first case we get two kinds of existence conditions of MOIS and two constructing methods for it, while in the second case we examine the mixed investigation strategies which can prevent the follower from misrepresentation, and then evaluate them from the leader's interests.