Agentic AI and Hallucinations

Referee: [§2] §2 (model primitives): the incentive-compatibility constraint for verification effort equates marginal cost to the discounted loss of all future rents only because the continuation value after a hallucination is set to zero for that user-agent pair. The paper should derive the equilibrium effort level explicitly under a positive continuation probability (e.g., user forgiveness or switching) and show whether the comparative static on the share of high-accuracy users survives; without this check the load-bearing role of the permanent-halt assumption remains untested.

Authors: We agree that the zero-continuation-value assumption after a detected hallucination is central to generating strict incentives for verification. This choice is motivated by the permanent reputational damage observed in professional domains. To address the concern directly, we will add an extension in the revised Section 2 that introduces a continuation probability γ ∈ (0,1) (capturing forgiveness or user switching). We derive the modified incentive-compatibility condition and show analytically that the equilibrium effort remains strictly increasing in the share of high-accuracy users provided γ is below a threshold that depends on the discount factor. The main comparative static therefore survives for plausible values of γ. revision: yes

Referee: [§3, Proposition 1] §3, Proposition 1: uniqueness of the reputational equilibrium is asserted under nontrivial discounting, yet the proof sketch is not supplied. The argument appears to rely on a contraction-mapping or fixed-point property of the best-reply correspondence; an explicit statement of the mapping and the conditions on the discount factor that guarantee uniqueness would allow readers to assess whether the result is robust to small changes in the user-type distribution.

Authors: We acknowledge that the uniqueness argument was only sketched. In the revision we will supply a complete proof in an appendix. We define the best-reply mapping T that sends a candidate effort profile to the optimal verification level given the induced continuation values. We then show that T is a contraction with modulus β(1-ε) < 1 whenever the discount factor β is sufficiently close to 1 and the type distribution satisfies a mild continuity condition. This establishes uniqueness and also clarifies the robustness to small perturbations in the user-type measure. revision: yes

Referee: [§4] §4 (comparative statics): the claim that equilibrium effort rises with the share of high-accuracy users follows from the shift in the effective continuation value when the population composition changes. The paper should report the derivative of equilibrium effort with respect to this share (or the relevant cross-partial) and confirm that it remains positive when the hallucination probability is allowed to depend on effort in a non-linear way.

Authors: We will report the explicit derivative de*/dμ in the revised Section 4, where μ denotes the measure of high-accuracy users. The sign is positive because an increase in μ raises the average continuation value that disciplines effort. For non-linear hallucination technologies (e.g., exponential or convex specifications), we will add a short analytical argument and a numerical illustration confirming that the relevant cross-partial remains positive under standard convexity of the verification cost function. These additions will be included in the revised manuscript. revision: partial