We study Bayesian persuasion when the receiver evaluates actions by reward-side Conditional Value-at-Risk (CVaR) rather than expected utility. CVaR preferences break the standard action-based direct-recommendation reduction: merging signals that recommend the same action can change the receiver's tail-risk ranking and destroy incentive compatibility. We show that this failure does not imply intractability in the explicit finite-state model. Each CVaR action value is max-affine in the posterior, and refining recommendations by the active affine piece yields an active-facet revelation principle and an exact polynomial-size linear program. We further identify a representation boundary: listed polyhedral risks remain tractable by the same LP, whereas succinctly represented facet families make exact persuasion NP-hard. Finally, we give a finite-precision approximation scheme for risk preferences determined by finitely many stable posterior statistics.

翻译：我们研究了当接收者依据行动奖励的条件风险价值（CVaR）而非期望效用进行评估时的贝叶斯说服问题。CVaR偏好打破了标准的基于行动的直接推荐简化：合并推荐相同行动的信号可能会改变接收者的尾部风险排序，并破坏激励相容性。我们证明这一失效并不意味着在显式有限状态模型中不可解。每个CVaR行动价值在后验上是最大仿射的，通过按照活跃仿射片段细化推荐，可得到一个活跃面启示原理和一个精确的多项式规模线性规划。我们进一步确定了一个表示边界：列举的多面体风险仍可通过相同LP处理，而简洁表示的facet族则使精确说服成为NP-hard问题。最后，我们为有限多个稳定后验统计量确定的风险偏好给出了一个有限精度近似方案。