arxiv: 2604.25696 · v1 · submitted 2026-04-28 · 🧮 math.OC · math.PR· stat.AP

Recognition: unknown

Holistic Decision-Making in Stopping Problems: Emphasizing Psychological Aspects

Georgy Sofronov , Joanna Rymaszewska , Krzysztof J. Szajowski

Authors on Pith no claims yet

Pith reviewed 2026-05-07 15:36 UTC · model grok-4.3

classification 🧮 math.OC math.PRstat.AP

keywords stopping gamesholistic decision-makingrationality deviationpsychological diagnosisMarkov momentsdecision strategiesrisk preferencesscenario analysis

0 comments

The pith

Deviations from rational stopping strategies in games serve as diagnostic indicators of players' psychological profiles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a holistic model for decision-making in stopping problems that incorporates probabilities of outcomes, associated payoffs, current state, historical data, potential future scenarios, strategic interactions with other players, flexibility to adapt as the game evolves, and integration of uncertainty through risk preferences and tolerances. It performs scenario analysis to evaluate different stopping times under varying conditions and connects this to ontological insights about decisions and strategies characterized by Markov moments. The central goal is to supply a theoretical basis for combining these factors into usable models and to implement the approach in psychological practice as a new method for assessing players' states.

Core claim

In a stopping game, a holistic decision-maker evaluates comprehensive information by assessing the probabilities of various outcomes and their associated payoffs, understanding the current state, historical data, and potential future scenarios, considering strategic interactions by anticipating other players' strategies, remaining flexible in adapting the strategy as the game evolves, integrating uncertainty by incorporating risk preferences and tolerances, and performing scenario analysis to evaluate the impact of different stopping times under varying conditions. The goal of this modeling is to introduce a novel method for assessing the state of players by leveraging deviations from the 'r

What carries the argument

The holistic decision-maker model that integrates probabilities, payoffs, history, strategic interactions, risk preferences, and scenario analysis to identify deviations from rational Markov stopping strategies.

Load-bearing premise

Deviations from rational stopping strategies can be reliably interpreted as diagnostic indicators of psychological profiles while the integrated model remains mathematically tractable.

What would settle it

An experiment that measures players' psychological profiles independently and finds no systematic correlation between those profiles and their observed deviations from rational stopping times in controlled games.

read the original abstract

Our research is closely related to ontological studies in mathematics. It provides crucial insights into the nature of decisions and strategies characterized by Markov moments. In a stopping game, a holistic decision-maker would evaluate comprehensive information by assessing the probabilities of various outcomes and their associated payoffs. This involves understanding the current state, historical data, and potential future scenarios. Such a decision-maker must also consider strategic interactions by anticipating and accounting for the strategies of other players. They must be flexible in adapting their strategy as the game evolves and able to integrate uncertainty by incorporating risk preferences and tolerances. They would perform scenario analysis to evaluate the impact of different stopping times under varying conditions. The goal of this modeling and its implementation in psychological practice is to introduce a novel method for assessing the state of players, leveraging deviations from rational strategies as diagnostic indicators of their psychological and decision-making profiles. The details of other models will be subject to contributed papers. The article presents the theoretical basis for combining various factors when modeling decision-making processes. The original title is "Rationality, Deviation, and Diagnosis: A Holistic Approach to Stopping Games" and will be used when it is possible to describe and interpret the results of the experiments we write about in the last section of the paper.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a high-level conceptual sketch for folding psychology into stopping problems via diagnostic deviations from rationality, but it contains no model, equations, or results to make the idea operational.

read the letter

The paper's main pitch is that a holistic decision-maker in a stopping game should weigh probabilities, history, other players' strategies, risk preferences, and scenarios together, then use any departures from the rational benchmark as signals of psychological state. That framing is the only real novelty on offer. It correctly notes that real decisions rarely isolate one factor at a time and that flexibility matters as the game evolves. The authors also flag that experiments are planned, which at least signals awareness that the idea needs grounding beyond description. Those points are fair as far as they go and could interest someone already working at the edge of stochastic control and behavioral work. Beyond the outline, though, the manuscript supplies nothing concrete. No value function appears, no recursive relation or algorithm shows how the listed factors are actually combined, and no check is given that the result stays tractable or that the deviations carry usable diagnostic content. The stress-test observation holds: without that construction it is impossible to verify the central claim. The text stays at the level of what a decision-maker 'would' consider, with the original title and the mention of future experiments indicating this version is preparatory rather than finished. Literature comparison is absent, so it is hard to judge how this sits against existing behavioral extensions of stopping theory. The piece is aimed at readers already thinking about interdisciplinary links between optimal stopping and psychology. Someone looking for theorems, simulations, or even a worked example will find little to use. I would not send it for peer review in this form. The authors should return with an explicit model and at least preliminary calculations or data before it warrants referee time.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a holistic decision-making framework for stopping problems that incorporates assessments of outcome probabilities and payoffs, current state and historical data, potential future scenarios, strategic interactions with other players, adaptability to evolving game conditions, integration of uncertainty via risk preferences, and scenario analysis for different stopping times. The primary objective is to establish a novel diagnostic method in psychological practice by interpreting deviations from rational stopping strategies as indicators of players' psychological and decision-making profiles. It presents the theoretical basis for combining these factors and notes that detailed models and experimental results will appear in subsequent papers.

Significance. A fully developed version of this framework could significantly advance the intersection of mathematical optimization and behavioral science by providing a structured way to model non-rational decision-making in dynamic games and use it for psychological assessment. However, as the current manuscript offers only a descriptive outline without any mathematical formalization, empirical validation, or specific derivations, its significance remains prospective rather than demonstrated.

major comments (2)

The central claim that deviations from rational strategies can serve as diagnostic indicators requires a well-defined holistic stopping rule. However, no value function, optimality equation, or integration mechanism is specified for combining the listed factors (probabilities, history, interactions, risk preferences, scenario analysis), making it impossible to evaluate tractability or the diagnostic utility (Abstract and theoretical basis description).
The paper states it presents the theoretical basis for combining various factors when modeling decision-making processes, but the description remains at a high level without equations, algorithms, or proofs, which is load-bearing for a contribution in mathematical optimization (theoretical basis section).

minor comments (2)

The manuscript refers to 'the last section of the paper' for experiments, but if this is the complete submission, those details are absent.
Consider providing references to foundational works in stopping theory (e.g., optimal stopping literature) to contextualize the holistic extension.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We acknowledge that the current work is at a conceptual stage, outlining a holistic framework for stopping problems with potential applications in psychological assessment. Below, we provide point-by-point responses to the major comments.

read point-by-point responses

Referee: The central claim that deviations from rational strategies can serve as diagnostic indicators requires a well-defined holistic stopping rule. However, no value function, optimality equation, or integration mechanism is specified for combining the listed factors (probabilities, history, interactions, risk preferences, scenario analysis), making it impossible to evaluate tractability or the diagnostic utility (Abstract and theoretical basis description).

Authors: We concur that without a specific value function, optimality equation, or explicit integration mechanism, a full assessment of tractability and diagnostic utility is not yet possible. This manuscript, however, is designed to present the theoretical basis at a high level by describing the factors a holistic decision-maker would consider and proposing that deviations from rational stopping times can indicate psychological profiles. As noted in the text, detailed models, including mathematical formalizations, algorithms, and experimental validations, are reserved for subsequent papers. The current contribution lies in introducing this interdisciplinary approach and its potential diagnostic value conceptually. revision: no
Referee: The paper states it presents the theoretical basis for combining various factors when modeling decision-making processes, but the description remains at a high level without equations, algorithms, or proofs, which is load-bearing for a contribution in mathematical optimization (theoretical basis section).

Authors: The manuscript explicitly states that it presents the theoretical basis for combining various factors, but clarifies that detailed models will be in contributed papers. Given the paper's focus on the holistic philosophy and its link to psychological diagnostics rather than providing a complete optimization framework at this time, we have kept the description at the conceptual level. We believe this is appropriate for establishing the idea before formal development. The absence of equations is intentional for this introductory piece. revision: no

Circularity Check

0 steps flagged

No mathematical derivations or equations present; purely conceptual framework

full rationale

The manuscript provides a high-level conceptual description of factors a holistic decision-maker would consider in stopping games (probabilities, history, interactions, risk preferences, scenario analysis) and states the goal of using deviations from rationality as psychological diagnostics. No value functions, Bellman equations, optimization procedures, or derivation chains are supplied in the text. Without any claimed mathematical steps that could reduce to fitted inputs, self-definitions, or self-citations, there are no load-bearing elements to inspect for circularity. The work remains at the level of outlining a theoretical basis rather than executing a derivation that could be tautological by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities are specified. The work appears to rest on standard concepts from stopping theory and psychology without detailing any additions or assumptions.

pith-pipeline@v0.9.0 · 5526 in / 1130 out tokens · 35575 ms · 2026-05-07T15:36:55.754386+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

28 extracted references · 20 canonical work pages

[1]

A multi-attribute exten- sion of the secretary problem: theory and experiments.J

Bearden, J.N., Murphy, R.O., Rapoport, A.: (2005). A multi-attribute exten- sion of the secretary problem: theory and experiments.J. Math. Psych.49(5), 410–422. doi: 10.1016/j.jmp.2005.08.002. MR 2173856 Cited on p. 2

work page doi:10.1016/j.jmp.2005.08.002 2005
[2]

Springer Finance

Bielecki, T.R., Rutkowski, M.: (2002).Credit risk: Modelling, valuation and hedging. Springer Finance. Berlin: Springer. doi: 10.1007/978-3-662-04821-

work page doi:10.1007/978-3-662-04821- 2002
[3]

Zbl 0979.91050 Cited on p. 6. 12 Georgy Sofronov, Joanna Rymaszewska, and Krzysztof J. Szajowski

work page arXiv
[4]

Mastering Mathematical Finance

Capi ´nski, M.J., Kopp, E.: (2014).Portfolio Theory and Risk Management. Mastering Mathematical Finance. Cambridge University Press, Cambridge. doi: 10.1017/CBO9781139017398. ISBN 978-1107-00367-5 Cited on p. 6

work page doi:10.1017/cbo9781139017398 2014
[5]

Houghton Mifflin Co., Boston, Mass

Chow, Y .S., Robbins, H., Siegmund, D.: (1971).Great expectations: the theory of optimal stopping. Houghton Mifflin Co., Boston, Mass. MR 0331675 Cited on p. 8

1971
[6]

Coombs, C.: (1975).Portfolio theory and the management of risk, pp. 63–

1975
[7]

doi: 10.1016/B978-0-12-397250-7.50009-X Cited on p

Academic Press, New York. doi: 10.1016/B978-0-12-397250-7.50009-X Cited on p. 6

work page doi:10.1016/b978-0-12-397250-7.50009-x
[8]

Average number of candidates surveyed by the headhunter in the recruitment.Math

Ernst, M., Szajowski, K.J.: (2021). Average number of candidates surveyed by the headhunter in the recruitment.Math. Appl. (Warsaw)49(1), 31–53. doi: 10.14708/ma.v49i1.7082. Zbl 1499.60128 Cited on pp. 2 and 9

work page doi:10.14708/ma.v49i1.7082 2021
[9]

Development of the schizophrenia concept and diagnostic tools for its assessment.Psychiatria PolskaXLII(4), 477–489

Frydecka, D., Kiejna, A.: (2008). Development of the schizophrenia concept and diagnostic tools for its assessment.Psychiatria PolskaXLII(4), 477–489. URLhttp://www.psychiatriapolska.pl/uploads/images/ PP_4_2008/Frydecka%20s477_Psychiatria%20Polska%204_ 2008.pdfCited on p. 6

2008
[10]

Recognizing the maximum of a sequence

Gilbert, J.P., Mosteller, F.: (1966). Recognizing the maximum of a sequence. J. Amer. Statist. Assoc.61, 35–73. doi: 10.1080/01621459.1966.10502008. MR 198637 Cited on p. 9

work page doi:10.1080/01621459.1966.10502008 1966
[11]

Libr., vol

Kozielecki, J.: (1981).Psychological decision theory.,Theory Decis. Libr., vol. 24. D. Reidel Publishing Company, Dordrecht. English Cited on p. 6

1981
[12]

A time-dependent best choice problem with costs and random lifetime in organ transplants.Appl

Krasnosielska, A.: (2010). A time-dependent best choice problem with costs and random lifetime in organ transplants.Appl. Math. (Warsaw)37(3), 257–

2010
[13]

MR 2684278 Cited on p

doi: 10.4064/am37-3-1. MR 2684278 Cited on p. 7

work page doi:10.4064/am37-3-1
[14]

Oxford: Oxford University Press

Leng, M.: (2010).Mathematics and reality. Oxford: Oxford University Press. Zbl 1209.00017 Cited on p. 2

work page arXiv 2010
[15]

Cowles Foundation for Research in Economics at Yale University, Monograph 16

Markowitz, H.M.: (1959).Portfolio selection: Efficient diversification of in- vestments. Cowles Foundation for Research in Economics at Yale University, Monograph 16. John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London. MR 0103768 Cited on p. 6

1959
[16]

Neurophysiological insights into sequential decision-making: exploring the secretary problem through ERPs and TBR dynamics.BMC Psychology12(1), 245

Mizrahi, D., Laufer, I., Zuckerman, I.: (2024). Neurophysiological insights into sequential decision-making: exploring the secretary problem through ERPs and TBR dynamics.BMC Psychology12(1), 245. doi: 10.1186/s40359- 024-01750-5 Cited on p. 11

work page doi:10.1186/s40359- 2024
[17]

Thinking and car- ing about cognitive inconsistency: when and for whom does attitudinal am- bivalence feel uncomfortable?J

Newby-Clark, I.R., Mcgregor, I., Zanna, M.P.: (2002). Thinking and car- ing about cognitive inconsistency: when and for whom does attitudinal am- bivalence feel uncomfortable?J. Pers. Soc. Psychol.82(2), 157–166. doi: 10.1037/0022-3514.82.2.157. PMID: 11831406 Cited on p. 6

work page doi:10.1037/0022-3514.82.2.157 2002
[18]

Nonzero-sum stochastic games

Nowak, A.S., Szajowski, K.: (1999). Nonzero-sum stochastic games. In: Stochastic and differential games. Theory and numerical methods. Dedicated to Prof. A. I. Subbotin, pp. 297–342. Boston: Birkhäuser. Zbl 0940.91014 Cited on p. 11. Holistic Decision-Making in Stopping Problems: Emphasizing Psychological Aspects 13

work page arXiv 1999
[19]

Penguin, New York, NY

Pinker, S.: (2021).Rationality: What It Is, Why It Seems Scarce, Why It Mat- ters.Penguin Books. Penguin, New York, NY . ISBN 978-0241380277 Cited on p. 6

2021
[20]

Sequential games with random priority

Radzik, T., Szajowski, K.: (1990). Sequential games with random priority. Sequential Analysis9(4). doi: 10.1080/07474949008836218 Cited on p. 11

work page doi:10.1080/07474949008836218 1990
[21]

Non-zero sum game with priority as Dynkin’s game.Math

Ravindran, G., Szajowski, K.: (1992). Non-zero sum game with priority as Dynkin’s game.Math. Japon.37(3), 401–413. Zbl 0763.90095 Cited on p. 11. [19]Ширяев, А.Н.: (1969).Статистический последовательный анализ. Оптимальные правила остановки.Optimisatsiya i Issledovanie Operatsi˘ı. Академиздатцентр “Наука”,Москва. doi: 10.1007/978-3-540-74011-

work page doi:10.1007/978-3-540-74011- 1992
[22]

Zbl 0214.45301, published in 1973 in series: Translations of Mathemati- cal Monographs. V ol. 38. Providence, R. I.: American Mathematical Society (AMS). iv, 174 pp.-trans. Lisa and Judah Rosenblatt. Cited on p. 8

work page arXiv 1973
[23]

The Generalized Stackelberg Equilib- rium of the Two-Person Stopping Game.Journal of the Operations Research Society of China12(1), 155–168

Skarupski, M., Szajowski, K.J.: (2024). The Generalized Stackelberg Equilib- rium of the Two-Person Stopping Game.Journal of the Operations Research Society of China12(1), 155–168. doi: 10.1007/s40305-023-00460-w Cited on p. 11

work page doi:10.1007/s40305-023-00460-w 2024
[24]

CRC Press, Taylor & Francis Group, United States

Sofronov, G., Szajowski, K.: (2025).Multiple stopping problems: unilateral and multilateral approaches. CRC Press, Taylor & Francis Group, United States. doi: 10.1201/9781003407102 Cited on p. 9

work page doi:10.1201/9781003407102 2025
[25]

Ocena praw- dopodobie´ nsta i modele wyboru w sytuacji ryzykownej

Sokołowska, J.: (2005).Psychologia decyzji ryzykownych. Ocena praw- dopodobie´ nsta i modele wyboru w sytuacji ryzykownej. Wydawnictwo Szkoły Wy˙zszej Psychologii SpołecznejAcademica, Warszawa. ISBN 978-83-8928- 114-2 Cited on p. 6

2005
[26]

Metacognitive Model of Ambivalence: The Role of Multiple Beliefs and Metacognitions in Creating Attitude Am- bivalence.Communication Theory25(1), 23–45

Song, H., Ewoldsen, D.R.: (2014). Metacognitive Model of Ambivalence: The Role of Multiple Beliefs and Metacognitions in Creating Attitude Am- bivalence.Communication Theory25(1), 23–45. doi: 10.1111/comt.12050 Cited on p. 6

work page doi:10.1111/comt.12050 2014
[27]

Analysis of heuristic solutions to the best choice problem.European J

Stein, W.E., Seale, D.A., Rapoport, A.: (2003). Analysis of heuristic solutions to the best choice problem.European J. Oper. Res.151(1), 140–152. doi: 10.1016/S0377-2217(02)00601-X. MR 1997012; Zbl 1043.90086 Cited on p. 11

work page doi:10.1016/s0377-2217(02)00601-x 2003
[28]

Duration of a secretary problem.J

Yeo, G.F.: (1997). Duration of a secretary problem.J. Appl. Probab.34(2), 556–558. doi: 10.1017/s0021900200101184. MR 1447359 Cited on p. 9

work page doi:10.1017/s0021900200101184 1997