Asymptotic structure of the optimal dynamic contract

Establish whether, in the repeated persuasion-with-transfers model described in Section 6 where Sender and Receiver interact indefinitely with an i.i.d. state each period and Sender commits to dynamic policies mapping histories to Bayesian experiments and nonnegative transfer schedules, the optimal contract asymptotically converges to either (i) the policy that repeats the static optimal information-plus-transfer design every period, or (ii) a full-information policy accompanied by a lump-sum transfer that services a utility promise constraint.

Background

The paper studies joint design of information and transfers in a finite-state, finite-action persuasion framework and extends the analysis to a dynamic setting with repeated interactions and i.i.d. states. In the static constrained problem (with an exogenous outside option), the authors show that optimal transfers take the form of canonical payments plus a lump-sum and that, when the lump-sum is positive, full information is optimal. This motivates a conjecture about the long-run structure of optimal dynamic policies.

In the dynamic section, the authors demonstrate that repetition does not necessarily restore ex-post efficiency and provide sufficient conditions under which Sender benefits from dynamics. However, they do not characterize the asymptotic form of optimal contracts. In the Discussion, they explicitly conjecture that the optimal contract converges either to the repeated static optimum or to full information with a utility-promising transfer, highlighting a concrete unresolved question about long-run behavior of optimal dynamic information-transfer policies.