Pricing time versus spending a state: two incompatible formalisations of rest

Question: How do computational models of motivational vigour and effort allocation formalise the trade-off between reward-seeking and recuperative rest during ongoing behaviour?

Answer

Across the retrieved papers, rest is almost never a first-class action in a choice model. The dominant formalisation keeps a scalar cost-benefit comparison and lets a latent fatigue state inflate the effort-cost term, so that recuperation appears only as the absence of an accepted offer rather than as a valued alternative with its own dynamics [3] [5]. A second, largely non-interacting family prices time instead of state — reward-rate maximisation with an opportunity cost per unit time — in which "rest" is simply any lower-rate activity competed against, and the identity of the rest interval never enters the equations [15]. The only formalisms in this corpus that genuinely endogenise the alternation between working and recuperating come from bout-length optimisation in patch-leaving and progressive-ratio designs, where the decision variable is how long to harvest before paying a travel/reset delay [6] [25]. Taken together, the field has the ingredients — asymmetric accumulation/recovery dynamics on one side, optimal stopping rules on the other — but no model in these results estimates recovery kinetics and rest choice as jointly determined quantities within a single agent.

Fatigue enters models as an asymmetric latent state whose recovery term is attached to rest, not to a decision

Fitting subjective ratings across three grip-force experiments, a model in which fatigue has a recoverable component that falls during rest and an unrecoverable component that rises only with exertion accounted best for trial-by-trial fluctuations in both fatigue and perceived effort [7]. In a 75-minute paradigm where participants repeatedly chose between resting and a demanding working-memory task, fatigue accumulated over time and pre-choice fatigue predicted avoidance of the effortful option despite high overall accuracy [4]. Rest is not merely passive decay: under mental fatigue, practice-block decrements in a finger-tapping task were compensated by larger gains during inter-block rest, with a strong negative correlation between online losses and offline gains [9]. Recovery also has a neural signature persisting beyond the rest period, with reduced ventromedial prefrontal–supramarginal connectivity at rest tracking heightened effort perception [29]. Crucially, fatigue is not a single quantity: two biofeedback conditions produced equal strength loss and equal felt fatigue, yet only the condition demanding compensatory neuromuscular activation raised the subjective cost of effort, implying separable components [13].

In choice models the state acts by inflating effort cost, leaving rest as a residual category

Computational modelling of choices made before and after a fatiguing working-memory task showed that cognitive exertion raises the subjective cost of prospective physical effort relative to a rested baseline [3]. Questionnaire-derived fatigue scores were more strongly associated with effort-based choice than depressed-mood scores in major depression, consistent with fatigue acting through perceived cost [5]. A four-parameter account validated across healthy, current-depressed and remitted groups dissociated overall acceptance bias from reward sensitivity and linear versus quadratic effort sensitivity, and located group differences in the acceptance bias rather than in effort sensitivity [19]. In depression the relevant deformation may be at the level of effort representation itself: Bayesian modelling of effort psychophysics showed compressed effort signals with reduced precision and increased reliance on priors [18]. Persistent post-COVID fatigue was associated with reduced reward sensitivity in effort-based choice rather than altered effort weighting [1]. This parameter-by-parameter decomposition is under pressure from evidence that effort avoidance does not generalise across paradigms, with individual avoidance tracking task-specific performance instead [21].

Pricing time is not the same as pricing recovery, and the control variable is contested

Reward-rate maximisation yields a formal expression in which the cost of time decomposes into an apportionment term and an opportunity-cost term, generating discounting functions that mix hyperbolic and linear components [15]. Optimal patch-leaving under exponential temporal discounting can predict either earlier or later departure than the marginal value theorem depending on discount rate and environment structure [26]. Direct evidence for the opportunity-cost controller is mixed: cognitive effort allocation was better explained by recent performance history than by average reward rate, and participants were insensitive to the reward currently at stake [16]. The two formalisms are also conceptually distinct rather than interchangeable — opportunity-cost models are explicitly medium-independent and carry no metabolic resource, which is what makes them hard to reconcile with resource-style fatigue states [20]. Learning of effort cost itself appears not to follow canonical temporal-difference updating but to be retrospective, updated at effort completion [22].

Bout-length optimisation is the only framework here that makes the work–rest switch the decision variable

Recasting the progressive-ratio task as a patch-leaving problem by adding a costly reset lever, with a computed optimal bout length maximising long-run reward rate, showed that rats adapted to the reset delay's cost but systematically over-harvested [6]. Rats given access to a food patch and a non-food "leisure" patch extended stay durations in both when travel cost was high, indicating shared rational principles across food and non-food goals [25]. Risk and environmental richness also shift allocation: with short travel delays rats spent more time in the low-variance option, and over-harvesting grew with successive visits to the same patch [23]. In humans, persistence versus disengagement in a sequential effort task was shaped jointly by difficulty, skill, time-on-task indexing fatigue, accumulated errors and goal proximity, with disengagement preceded by abrupt short-term performance decline [28]. Neural work identifies a persistence signal that fits this framing: inhibiting anterior cingulate cortex reduced lever presses and lowered breakpoints in effort choices without changing reward latencies, leaving motivational value intact [2].

Vigour models and applied fatigue models each capture one half of the trade-off and drop the other

Vigour research formalises behaviour as minimising a time cost rather than a fatigue state: reach and harvest durations were largely decoupled and were better predicted by separate but interdependent optimisations with distinct, history-sensitive time costs than by a single global-utility model [24], while macaque decision–action coordination approximated the single-trial reward-rate optimum [27]. Reach vigour tracked both reward expectation and reward prediction error at short latency [14], and dorsal versus ventral striatal lesions dissociated effort-sensitive speed from reward-seeking urgency [17]. Conversely, applied models carry explicit recovery kinetics but treat rest as an exogenous schedule input: constrained Markov decision processes with online-estimated fatigue-recovery parameters constrain task allocation to keep fatigue within safe limits [11]; a three-compartment fatigue model with recovery supplies the optimisation signal for interface layout [12]; and impulse-response fitness–fatigue models, when optimised, yield the degenerate policy of maximal training followed by complete cessation unless nonlinear modifications are added [8] [10].

Conflicts and gaps

The central disagreement is over what the state variable is for. Resource-style accounts posit a recoverable quantity depleted by exertion and restored by rest [7], whereas opportunity-cost accounts explicitly deny any medium-specific resource [20], and within-task performance declines have been attributed to allocation adjustments rather than depletion [30]. A second conflict concerns the controller: average reward rate [15] versus recent performance history [16] versus retrospective cost updating [22]. Unresolved: no retrieved model estimates a recovery time constant as a free parameter jointly with choices between working and resting; rest durations are usually imposed rather than chosen; and the systematic over-harvesting observed in bout-length tasks [6] [23] has not been shown to reflect under-weighted recovery value rather than noisy valuation.

What would change the answer

A paradigm in which both whether to rest and how long to rest are chosen, with reward rate manipulated orthogonally to accumulated fatigue, and formal comparison of three nested models — static fatigue-inflated effort cost, dynamic state with endogenous rest, and pure opportunity cost — would discriminate the accounts directly. Estimating recovery rate from rest choices and then predicting independent effort choices from that estimate would test whether the same state variable drives both. Pharmacological or lesion dissociations of accumulation from recovery, combined with the striatal and cingulate manipulations already available [17] [2], would establish whether the two halves of the trade-off share a valuation substrate. Finally, importing the fatigue-state dynamics of [7] into the bout-length optimisation of [6] would yield a single model whose optimal policy specifies rest, not merely departure.

References

[1] Scholing, J. M., Lambregts, B. I. H. M., van den Bosch, R., Aarts, E., van der Schaaf, M. E.. "Fatigue >12 weeks after coronavirus disease (COVID) is associated with reduced reward sensitivity during effort-based decision making". bioRxiv. 2024-11-06T00:00:00.000Z. URL: https://doi.org/10.1101/2024.11.04.621806

[2] Gonzalez, V. V., Malvaez, M., Yeghikian, A., Wissing, S., Sharpe, M., Wassum, K. M., Izquierdo, A.. "A common stay-on-goal mechanism in anterior cingulate cortex for information and effort choices". bioRxiv. 2025-01-19T00:00:00.000Z. URL: https://doi.org/10.1101/2024.10.23.619920

[3] Dryzer, M., Chib, V. S.. "Neural mechanisms underlying the effects of cognitive fatigue on physical effort-based decision-making". bioRxiv. 2024-12-11T00:00:00.000Z. URL: https://doi.org/10.1101/2024.12.06.627274

[4] Yang Yang, Akina Umemoto, Senne Braem, Clay Holroyd. "A transdiagnostic computational account linking mental fatigue and cognitive effort". psyarxiv. 2026-10-03T14:27:35.932Z. URL: https://osf.io/98pfs_v1

[5] Steward, G., Culbreth, A., Goes, F., Chib, V.. "Fatigue Symptoms Influence Effort-Based Decision-Making in Major Depressive Disorder". medRxiv. 2025-10-31T00:00:00.000Z. URL: https://doi.org/10.1101/2025.10.30.25338913

[6] Rivera, Z. M. G., Guerrero Leon, K., Cervera, M., Aguayo, B., Izquierdo, A., Wikenheiser, A. M.. "A progressive ratio task with costly resets reveals adaptive effort-delay tradeoffs". bioRxiv. 2025-06-06T00:00:00.000Z. URL: https://doi.org/10.1101/2025.06.03.657635

[7] Tanja Müller, Joseph Milton, Masud Husain, Matthew Apps. "Computational signatures of exertion and rest underlie moment-to-moment dynamics of subjective perceptions of effort and fatigue". psyarxiv. 2025-03-06T15:07:22.320Z. URL: https://doi.org/10.3758/s13415-026-01417-1

[8] David Ceddia, Howard Bondell, Peter Taylor. "Mathematical Modelling and Optimisation of Athletic Performance: Tapering and Periodisation". arxiv. 2026-08-24T00:00:00.000Z. URL: https://doi.org/10.1515/jqas-2025-0077

[9] Ruffino, C., Jacquet, T., Lepers, R., Papaxanthis, C., Truong, C.. "Motor learning under mental fatigue: the compensatory role of rest periods". bioRxiv. 2026-03-24T00:00:00.000Z. URL: https://doi.org/10.64898/2026.03.21.713370

[10] Jacky Montmain, Pierre Couturier, Gérard Dray. "New perspectives for the fitness fatigue model: how to revisit questions about the science of sports training from the perspective of systems control theory". arxiv. 2026-09-23T00:00:00.000Z. URL: https://arxiv.org/abs/2609.26506

[11] Jintao Xue, Xiao Li, Nianmin Zhang. "Safe reinforcement learning with online filtering for fatigue-predictive human-robot task planning and allocation in production". arxiv. 2026-04-17T00:00:00.000Z. URL: https://doi.org/10.1016/j.jmsy.2025.12.019

[12] Harshitha Voleti, Charalambos Poullis. "Designing Fatigue-Aware VR Interfaces via Biomechanical Models". arxiv. 2026-03-30T00:00:00.000Z. URL: https://arxiv.org/abs/2603.26031

[13] Casamento-Moran, A., Kim, A., Lee, J. L., Chib, V. S.. "Neuromuscular Signals Shape Fatigue and Effort-Based Decision-Making in Humans". bioRxiv. 2026-03-09T00:00:00.000Z. URL: https://doi.org/10.64898/2025.12.06.692763

[14] Korbisch, C. C., Ahmed, A. A.. "Rapid Dopaminergic Signatures in Movement: Reach Vigor Reflects Reward Prediction Error and Learned Expectation". bioRxiv. 2025-05-20T00:00:00.000Z. URL: https://doi.org/10.1101/2025.03.24.645035

[15] Sutlief, E., Walters, C., Marton, T., Hussain Shuler, M. G.. "The value of initiating a pursuit in temporal decision-making". bioRxiv. 2024-11-22T00:00:00.000Z. URL: https://doi.org/10.1101/2024.06.16.599189

[16] Spronkers, F. S., Koolschijn, R. S., Daw, N. D., Otto, A. R., den Ouden, H. E. M.. "Dissecting the contribution of recent reward versus recent performance history on cognitive effort allocation". bioRxiv. 2025-07-11T00:00:00.000Z. URL: https://doi.org/10.1101/2025.07.08.663681

[17] Morvan, T., Timmel, Z., Eloy, C., Robbe, D.. "Complementary contributions of dorsal and ventral striatum to cost-benefit vigor adaptations". bioRxiv. 2026-06-10T00:00:00.000Z. URL: https://doi.org/10.1101/2024.05.31.596850

[18] Harlev, D., Wolpe, N.. "Not just harder: Compression of perceived effort in major depressive disorder is associated with symptom burden and altered decision-making". medRxiv. 2026-10-14T00:00:00.000Z. URL: https://doi.org/10.64898/2026.10.13.26365398

[19] Valton, V., Mkrtchian, A., Moses-Payne, M., Gray, A., Kieslich, K., VanUrk, S., Samborska, V., Halahakoon, D. C., Manohar, S. G., Dayan, P., Husain, M., Roiser, J. P.. "A computational approach to understanding effort-based decision-making in depression". bioRxiv. 2025-08-26T00:00:00.000Z. URL: https://doi.org/10.1101/2024.06.17.599286

[20] Jake Embrey. "Metabolic constraints may both help and hinder cognitive models". psyarxiv. 2026-04-30T23:46:13.451Z. URL: https://osf.io/be7at_v1

[21] Sean Devine, Mario Bogdanov, Laura Bustamante, Ziqi Fu, Madeleine Sharp, A. Otto. "No Evidence for a Generalized Construct of Cognitive Effort Avoidance". psyarxiv. 2025-08-12T16:51:06.851Z. URL: https://osf.io/km53v_v1

[22] Mitsuto, A., Akaishi, R., Onoda, K., Morita, K., Kawagoe, T., Yamamoto, T., Yamaguchi, S., Hanajima, R., Westbrook, A.. "Mental Effort Cost Learning is Retrospective". bioRxiv. 2025-10-20T00:00:00.000Z. URL: https://doi.org/10.1101/2022.11.26.518013

[23] Garcia, M., Wikenheiser, A. M.. "Risk preferences depend on environmental richness in rats performing a patch-foraging task". bioRxiv. 2025-02-04T00:00:00.000Z. URL: https://doi.org/10.1101/2025.02.04.636458

[24] Conessa, A., Boutin, A., Berret, B.. "Evidence for flexible regulation of movement and decision vigor in a reward-oriented task". bioRxiv. 2026-07-20T00:00:00.000Z. URL: https://doi.org/10.1101/2025.11.25.690375

[25] Logue, R. S., Garcia, A. K., Bejarano, B. A., Fujioka, T., Duke, M., Kendall, R. K., Wikenheiser, A. M.. "Rats pursue food and leisure following the same rational principles". bioRxiv. 2025-07-31T00:00:00.000Z. URL: https://doi.org/10.1101/2024.12.08.627420

[26] Zylberberg, J.. "Should I stay or should I go? Generalized marginal value theorem with temporal discounting". bioRxiv. 2024-10-28T00:00:00.000Z. URL: https://doi.org/10.1101/2024.10.28.620618

[27] Saleri, C., Gardechaux, G., Foncelle, A., Thura, D.. "Optimal foraging requires coordinating decisions with movements". bioRxiv. 2025-09-19T00:00:00.000Z. URL: https://doi.org/10.1101/2025.09.19.677254

[28] Chaigneau, A., Moretti, R., Iodice, P., Pessiglione, M., Pezzulo, G.. "Determinants of persistence in sequential effort-based decision-making". bioRxiv. 2026-05-14T00:00:00.000Z. URL: https://doi.org/10.64898/2026.05.11.723817

[29] John Read, Camille Guillemin, Maëlle Charonitis, Florence Requier, Nikita Beliy, Mohamed Bahri, gilles vandewalle, Fabienne Collette. "Effort and motivation to characterize mental fatigue: behavior and functional connectivity". psyarxiv. 2025-07-01T11:56:12.132Z. URL: https://doi.org/10.1037/mot0000421

[30] Aviv Emanuel. "Computational underpinnings of cognitive effortful performance in short timescales". psyarxiv. 2025-06-18T17:42:04.829Z. URL: https://osf.io/zqgy6_v2

How this survey was made

This survey answers one question: “How do computational models of motivational vigour and effort allocation formalise the trade-off between reward-seeking and recuperative rest during ongoing behaviour?”

We keep our own collection of recent preprints and refresh it every day from bioRxiv, medRxiv, arXiv, PsyArXiv, SocArXiv and ChemRxiv. For each survey, we search that collection for recent work and keep the strongest matches: papers that use the same terms as the question, and papers on the same topic in different words.

The text was written from the titles and abstracts of those papers; the full texts were not read. Statements that draw on a particular paper are marked with a number in brackets. The reference list just above is the 30 papers whose work this text draws on, chosen from the 144 papers those searches returned; the rest of the shortlist is not printed. It is not a complete review of everything published on the question.

Treat this as a starting point and a reading list, not a peer-reviewed review. The searches behind this survey ran on October 21, 2026 and covered work from the previous two years.