Accelerator and Brake: Dynamic Persuasion with Dead Ends

TL;DR

The paper studies dynamic Bayesian persuasion in a continuous-time bandit with nonmonotone preferences over the agent's stopping time, where the principal privately observes project quality and uses information disclosure to steer the agent's stopping decision.It develops a two-stage, milestone-based framework that decomposes the problem into a motivation subproblem before the principal's ideal stopping time t* and a dissuasion subproblem after t*, solving each stage under incentive compatibility constraints.A key result is that the optimal policy involves at most two one-shot disclosures an accelerator before t* and a brake after t*, with gradual disclosure possible in an interval when time-risk aversion differs locally between the principal and the agent, as captured by Arrow-Pratt coefficients.The analysis provides a tractable, risk-sharing interpretation of persuasion patterns through the Arrow-Pratt statistic, derives the value of dynamic commitment, and discusses applications to non-transferable incentive settings such as R&D management, career transitions, and academic supervision.

Abstract

We study optimal dynamic persuasion in a bandit experimentation model where a principal, unlike in standard settings, has a single-peaked preference over the agent's stopping time. This non-monotonic preference arises because maximizing the agent's effort is not always in the principal's best interest, as it may lead to a dead end. The principal privately observes the agent's payoff upon success and uses the information as the instrument of incentives. We show that the optimal dynamic information policy involves at most two one-shot disclosures: an accelerator before the principal's optimal stopping time, persuading the agent to be optimistic, and a brake after the principal's optimal stopping time, persuading the agent to be pessimistic. A key insight of our analysis is that the optimal disclosure pattern -- whether gradual or one-shot -- depends on how the principal resolves a trade-off between the mean of stopping times and its riskiness. We identify the Arrow-Pratt coefficient of absolute risk aversion as a sufficient statistic for determining the optimal disclosure structure.

Figures (7)

• Figure 1: The optimal static disclosure: The solid curve represents the principal's payoff function $W_{\text{NI}}(\mu)$, with the shaded area as its convex hull. The two dashed lines form its concave closure, which indicates the maximally achievable payoff through persuasion.
• Figure 2: The structure of the optimal dynamic information policy.
• Figure 3: Comparative statics. Panel (a) shows the disclosure probabilities ($x_a, x_b$). Panel (b) shows the disclosure times ($t_a, t_b$). The vertical dashed lines indicate the belief thresholds identified in Proposition 2.
• Figure 4: A typical example of the CDF of the optimal information policy before $t^*$ with gradual disclosure, where $\underline{t}_g>\tau(\mu_0)$. The dashed curve is the optimal stopping time lottery $F_L^*(t)$ given by (\ref{['eq.closeform']}).
• Figure 5: The potential optimal structures.

Theorems & Definitions (22)

• Proposition 1
• proof
• Theorem 1
• proof
• Proposition 2
• proof
• Lemma 1
• Proposition 3
• proof
• Proposition 4