{"id":"abcd9264-e8be-4f3b-b997-376f86e2826e","arxiv_id":"2606.00970","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Bellman optimality in MDPs with absorbing catastrophic states generates prospect-theory signatures including S-shaped value functions and endogenous loss aversion from risk-neutral linear-reward agents.","lead":"This paper shows that standard Bellman optimality in Markov decision processes with an absorbing catastrophic state produces S-shaped value functions, endogenous loss aversion, and reflection-effect policy reversals even for risk-neutral agents using linear rewards. A smart generalist might read it to see how environmental structure with ruin risk can generate apparent behavioral biases without any psychological assumptions.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"Reader correctly flags the absorbing state as the load-bearing structural feature; because the paper treats it as the deliberate sufficient condition and supplies matching closed-form plus numerical evidence, the argument holds without adjustment.","tokens_in":1930,"tokens_out":236,"duration_ms":15480,"concrete_test":"Independently re-derive the asymptotic \bar{\bar{\beta}} expression from the Bellman equation in the far-field limit (V(s)≈c·s) and near-catastrophe limit without using the paper's intermediate identities; check whether the resulting formula matches the reported dependence on p, r, β.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on the absorbing catastrophic state altering Bellman recursion to produce the S-shape, endogenous λ*(S)>1, and reflection effect under linear rewards. The closed-form \bar{\bar{\beta}} derivation, R²=0.999 match, and robustness to Q-learning plus multiple noise distributions are internally consistent with this mechanism; the absorbing-state condition is the explicit, not hidden, premise.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper claims that in MDPs with an absorbing catastrophic state, Bellman optimality under linear rewards and risk-neutral agents produces three prospect-theory signatures: an S-shaped value function (convex near catastrophe, concave far-field), endogenous loss aversion with λ*(S)>1, and reflection-effect policy reversals. It derives a closed-form asymptotic loss-aversion plateau \bar λ(p,r,β) that matches numerical solutions to R²=0.999 across 495 configurations, shows the asymmetry contribution to \bar λ is small (median 4.6% at r=1.25), and demonstrates persistence under tabular Q-learning (V* correlations 0.98/1.00) and stochastic noise (Gaussian, t_3, skew-normal) up to 50% step size, with plateau tracking within 0.41–9.6%.","tokens_in":2018,"tokens_out":456,"duration_ms":27032,"significance":"If the central derivation holds, the result is significant: it identifies the absorbing catastrophic state as a minimal structural mechanism sufficient to generate prospect-theory-like behavior from standard optimal control, without utility curvature, probability weighting, or external data fitting. The parameter-free closed-form, R²=0.999 numerical match, and robustness to model-free learning plus multiple noise distributions constitute strong internal validation. This provides a clean bridge between rational MDP theory and behavioral signatures, with the explicit premise (absorbing failure) stated throughout.","major_comments":[],"minor_comments":[{"comment":"Abstract: the median asymmetry share (4.6% at r=1.25, 13.9% at r=2) is reported across a (p,β) sweep; adding the exact number of cells or grid resolution would aid interpretation of the 'every cell tested' claim.","section":"Abstract"},{"comment":"The noise-robustness paragraph states tracking 'within 0.41% for safe-channel noise and within 9.6% for risky-channel or both-channel noise'; a short table or explicit per-distribution errors would improve quantitative clarity.","section":null}],"recommendation":"accept","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their positive assessment, accurate summary of the results, and recommendation to accept the manuscript. No major comments require response.","responses":[],"tokens_in":1485,"tokens_out":47,"duration_ms":7443,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The key point is that this paper shows standard Bellman optimality in MDPs with an absorbing catastrophic state generates an S-shaped value function, endogenous loss aversion above one, and reflection-effect policy reversals even with linear rewards and no probability weighting. The closed-form for the asymptotic loss-aversion plateau depends only on win probability, payoff asymmetry, and discount factor, and it matches numerical solutions to R-squared 0.999 across 495 configurations.\n\nWhat the work does well is derive the result directly from the MDP equations without fitting to external data, then confirm it holds under tabular Q-learning at high correlation and under Gaussian, Student-t, and skew-normal noise. The boundary effect from the absorbing state dominates the asymmetry contribution in every tested cell, which is a clean quantitative finding. The absorbing-state premise is stated explicitly as the driver, so there is no hidden circularity.\n\nThe main soft spot is that the demonstrations stay in simple chain MDPs; whether the signatures persist in higher-dimensional or continuous spaces is left open, though that is a natural extension rather than a flaw in the current argument. The robustness to model-free learning and noise is reassuring but still within controlled synthetic settings.\n\nThis is for researchers working at the intersection of sequential decision making and behavioral patterns, especially in AI safety or economics contexts where permanent failure states matter. It shows clear thinking on how environment structure alone can induce the observed signatures. It deserves peer review.","headline":"Bellman optimality in MDPs with absorbing catastrophes produces prospect-theory signatures from linear rewards via the recursion structure.","tokens_in":2510,"tokens_out":356,"would_cite":true,"duration_ms":17654,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Bellman optimality in MDPs with an absorbing catastrophic state produces an S-shaped value function, endogenous loss aversion greater than one, and reflection-effect policy reversals even with linear rewards.","keywords":["Markov decision processes","Bellman optimality","absorbing states","catastrophic failure","loss aversion","prospect theory signatures","policy reversal","S-shaped value function"],"falsifier":"Modify the MDP so the catastrophic state is no longer absorbing, allow escape with positive probability, recompute the optimal value function, and check whether the S-shape, λ*(S) > 1, and policy reversal all disappear.","tokens_in":2818,"feed_emoji":"⚠","tokens_out":752,"duration_ms":16979,"temperature":0.7,"pith_summary":"The paper establishes that Markov decision processes containing an absorbing catastrophic state generate three prospect-theory signatures under ordinary risk-neutral optimal control. The value function becomes convex near the catastrophe and concave at higher states, an endogenous loss-sensitivity coefficient exceeds one, and optimal policies reverse their risk preference depending on whether the environment trends toward growth or decline. A closed-form expression for the long-run loss-aversion plateau is derived that depends only on win probability, payoff asymmetry ratio, and discount factor, and it matches numerical solutions to high accuracy. The same signatures appear when the agent is trained with tabular Q-learning and when transitions include Gaussian, heavy-tailed, or skewed noise.","feed_headline":"Absorbing catastrophes induce S-shaped values and λ>1 under Bellman optimality","feed_subtitle":"Linear-reward MDPs with failure states that end the episode produce convex-concave profiles, endogenous loss sensitivity above one, and risk","key_machinery":"The absorbing catastrophic state, which once entered keeps the agent there indefinitely with no escape or further positive rewards, altering the recursive value computation.","core_discovery":"In Markov decision processes with an absorbing catastrophic state, standard Bellman optimality yields an S-shaped value-function profile (convex near catastrophe, concave in the far field), an endogenous loss-sensitivity coefficient λ*(S) > 1, and a reflection-effect policy reversal, even though rewards remain linear and the agent has no utility curvature, probability weighting, or framing dependence.","pith_inferences":["Environmental structure alone can produce apparent risk attitudes that look like internal utility curvature, suggesting experiments that vary absorption while holding reward linearity fixed.","The same absorbing-state mechanism may operate in safety-critical control problems where failure terminates the episode, offering a structural account for observed caution without added behavioral parameters.","Extending the closed-form plateau expression to continuous-state or partially observable settings would test whether absorption remains sufficient when the state space changes."],"forward_implications":["Near the catastrophe the optimal policy selects the safe action in positive-drift regimes even when the risky action has higher immediate expected reward.","Near the catastrophe the optimal policy selects the risky action in negative-drift regimes even when the safe action has lower immediate expected loss.","The asymptotic loss-aversion plateau depends only on win probability, payoff asymmetry ratio, and discount factor, with asymmetry contributing a median 4.6 percent to 13.9 percent of the elevation above one across tested ratios.","The signatures survive model-free tabular Q-learning and persist when transition noise reaches 50 percent of step size in Gaussian, Student-t, or skew-normal distributions."],"fun_headline_variants":["Bellman optimality yields S-shaped values near catastrophes","Endogenous loss aversion arises in catastrophic MDPs","S-shaped value profiles from Bellman optimality in MDPs","Reflection effect appears in optimal policies with catastrophe"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The catastrophic state must be absorbing so that entry ends all future positive rewards.","fun_headline_variants_meta":{"raw":{"variants":["Bellman optimality yields S-shaped values near catastrophes","Endogenous loss aversion arises in catastrophic MDPs","S-shaped value profiles from Bellman optimality in MDPs","Reflection effect appears in optimal policies with catastrophe"]},"model":"grok-4.3","cost_usd":0.00973,"raw_usage":{"total_tokens":4414,"prompt_tokens":829,"num_sources_used":0,"completion_tokens":58,"cost_in_usd_ticks":97299500,"prompt_tokens_details":{"text_tokens":829,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3527,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":829,"tokens_out":58,"duration_ms":30794,"temperature":1.0,"reasoning_tokens":3527,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-01T07:23:15.687716+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Modify the MDP so the catastrophic state is no longer absorbing, allow escape with positive probability, recompute the optimal value function, and check whether the S-shape, λ*(S) > 1, and policy reversal all disappear.","supporting_citations":[],"review_version":2}