  We consider a Stackelberg game in which a principal (she) establishes a
two-stage contract with a non-myopic agent (he) whose type is unknown. The
contract takes the form of an incentive function mapping the agent's
first-stage action to his second-stage incentive. While the first-stage action
reveals the agent's type under truthful play, a non-myopic agent could benefit
from portraying a false type in the first stage to obtain a larger incentive in
the second stage. The challenge is thus for the principal to design the
incentive function so as to induce truthful play. We show that this is only
possible with a constant, non-reactive incentive functions when the type space
is continuous, whereas it can be achieved with reactive functions for discrete
types. Additionally, we show that introducing an adjustment mechanism that
penalizes inconsistent behavior across both stages allows the principal to
design more flexible incentive functions.
