Bayesian Persuasion with a Risk-Conscious Receiver
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914558429364224 |
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| author | Chen, Yujing |
| author_facet | Chen, Yujing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12094 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian Persuasion with a Risk-Conscious Receiver Chen, Yujing Computer Science and Game Theory Theoretical Economics 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. |
| title | Bayesian Persuasion with a Risk-Conscious Receiver |
| topic | Computer Science and Game Theory Theoretical Economics |
| url | https://arxiv.org/abs/2605.12094 |