{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T07:19:17Z","timestamp":1775027957379,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009217","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,9,21]],"date-time":"2021-09-21T00:00:00Z","timestamp":1632182400000}}],"reference-count":35,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T00:00:00Z","timestamp":1631145600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009708","name":"Novo Nordisk Fonden","doi-asserted-by":"crossref","award":["NNF14OC0011413"],"award-info":[{"award-number":["NNF14OC0011413"]}],"id":[{"id":"10.13039\/501100009708","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003554","name":"Lundbeckfonden","doi-asserted-by":"publisher","award":["R59 A5399"],"award-info":[{"award-number":["R59 A5399"]}],"id":[{"id":"10.13039\/501100003554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003554","name":"Lundbeckfonden","doi-asserted-by":"publisher","award":["R186-2015-2138"],"award-info":[{"award-number":["R186-2015-2138"]}],"id":[{"id":"10.13039\/501100003554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003554","name":"Lundbeckfonden","doi-asserted-by":"publisher","award":["R140-2013-13057"],"award-info":[{"award-number":["R140-2013-13057"]}],"id":[{"id":"10.13039\/501100003554","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004836","name":"Det Frie Forskningsr\u00e5d","doi-asserted-by":"crossref","award":["12-126925"],"award-info":[{"award-number":["12-126925"]}],"id":[{"id":"10.13039\/501100004836","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100009708","name":"Novo Nordisk Fonden","doi-asserted-by":"publisher","award":["NNF16OC0023090"],"award-info":[{"award-number":["NNF16OC0023090"]}],"id":[{"id":"10.13039\/501100009708","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To optimize wealth over time, agents should adapt their utility function according to the dynamical setting they face. Linear utility is optimal for additive dynamics, whereas logarithmic utility is optimal for multiplicative dynamics. Whether humans approximate time optimal behavior across different dynamics is unknown. Here we compare the effects of additive versus multiplicative gamble dynamics on risky choice. We show that utility functions are modulated by gamble dynamics in ways not explained by prevailing decision theories. Instead, as predicted by time optimality, risk aversion increases under multiplicative dynamics, distributing close to the values that maximize the time average growth of in-game wealth. We suggest that our findings motivate a need for explicitly grounding theories of decision-making on ergodic considerations.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009217","type":"journal-article","created":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T18:17:29Z","timestamp":1631211449000},"page":"e1009217","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":14,"title":["Ergodicity-breaking reveals time optimal decision making in humans"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9689-0869","authenticated-orcid":true,"given":"David","family":"Meder","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Finn","family":"Rabe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1079-9891","authenticated-orcid":true,"given":"Tobias","family":"Morville","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8606-7641","authenticated-orcid":true,"given":"Kristoffer H.","family":"Madsen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3411-5036","authenticated-orcid":true,"given":"Magnus T.","family":"Koudahl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ray J.","family":"Dolan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hartwig R.","family":"Siebner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3139-4324","authenticated-orcid":true,"given":"Oliver J.","family":"Hulme","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2021,9,9]]},"reference":[{"key":"pcbi.1009217.ref001","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1017\/CBO9781139381444.009","volume-title":"Wissenschaftliche Abhandlungen","author":"L Boltzmann","year":"2012"},{"key":"pcbi.1009217.ref002","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1063\/1.3127948","article-title":"Modern ergodic theory","volume":"26","author":"JL Lebowitz","year":"2008","journal-title":"Physics Today"},{"key":"pcbi.1009217.ref003","article-title":"The time interpretation of expected utility theory","author":"O Peters","year":"2018","journal-title":"ArXiv:180103680 [q-Fin]"},{"key":"pcbi.1009217.ref004","doi-asserted-by":"crossref","first-page":"023103","DOI":"10.1063\/1.4940236","article-title":"Evaluating gambles using dynamics","volume":"26","author":"O Peters","year":"2016","journal-title":"Chaos"},{"key":"pcbi.1009217.ref005","volume-title":"Theory of games and economic behaviour","author":"J von Neumann","year":"1947"},{"key":"pcbi.1009217.ref006","volume-title":"Foundations of economic analysis","author":"PA Samuelson","year":"1947"},{"key":"pcbi.1009217.ref007","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF00122574","article-title":"Advances in prospect theory: Cumulative representation of uncertainty","volume":"5","author":"A Tversky","year":"1992","journal-title":"J Risk Uncertainty"},{"key":"pcbi.1009217.ref008","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2307\/1914185","article-title":"Prospect Theory: An Analysis of Decision under Risk","volume":"47","author":"D Kahneman","year":"1979","journal-title":"Econometrica"},{"key":"pcbi.1009217.ref009","first-page":"90","article-title":"The theory of risk aversion","author":"KJ Arrow","year":"1971","journal-title":"Essays in the Theory of Risk-Bearing"},{"key":"pcbi.1009217.ref010","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1016\/j.neuroimage.2012.04.018","article-title":"Ten ironic rules for non-statistical reviewers","volume":"61","author":"K Friston","year":"2012","journal-title":"NeuroImage"},{"key":"pcbi.1009217.ref011","author":"H Markowitz","year":"1952","journal-title":"The Utility of Wealth"},{"key":"pcbi.1009217.ref012","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/s11166-006-8289-6","article-title":"Cumulative prospect theory\u2019s functional menagerie","volume":"32","author":"HP Stott","year":"2006","journal-title":"J Risk Uncertainty"},{"key":"pcbi.1009217.ref013","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.jmp.2010.08.006","article-title":"Hierarchical Bayesian parameter estimation for cumulative prospect theory","volume":"55","author":"H Nilsson","year":"2011","journal-title":"Journal of Mathematical Psychology"},{"key":"pcbi.1009217.ref014","volume-title":"Bayesian Cognitive Modeling","author":"MD Lee","year":"2009"},{"key":"pcbi.1009217.ref015","doi-asserted-by":"crossref","first-page":"e1003441","DOI":"10.1371\/journal.pcbi.1003441","article-title":"VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data","volume":"10","author":"J Daunizeau","year":"2014","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1009217.ref016","volume-title":"Theory of probability","author":"H Jeffreys","year":"1961","edition":"3"},{"key":"pcbi.1009217.ref017","unstructured":"van Doorn J, Derks K, Draws T, Etz A, Gronau QF, Haaf JM, et al. The JASP Guidelines for Conducting and Reporting a Bayesian Analysis n.d.:38."},{"key":"pcbi.1009217.ref018","doi-asserted-by":"crossref","first-page":"63","DOI":"10.12688\/wellcomeopenres.15191.1","article-title":"Raincloud plots: a multi-platform tool for robust data visualization","volume":"4","author":"M Allen","year":"2019","journal-title":"Wellcome Open Res"},{"key":"pcbi.1009217.ref019","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1109\/TIT.1956.1056803","article-title":"A new interpretation of information rate","volume":"2","author":"JL Kelly","year":"1956","journal-title":"Information Theory, IRE Transactions On"},{"key":"pcbi.1009217.ref020","author":"J Hjortsberg","year":"2019","journal-title":"Accuracy in sensory cue discrimination under additive and multiplicative dynamics"},{"key":"pcbi.1009217.ref021","unstructured":"Behavior Research Methods 2014 Wagenmakers n.d."},{"key":"pcbi.1009217.ref022","first-page":"76","article-title":"De Gustibus Non Est Disputandum","volume":"67","author":"G Stigler","year":"1977","journal-title":"American Economic Review"},{"key":"pcbi.1009217.ref023","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1111\/j.1468-2354.2008.00507.x","article-title":"Lost in state space: are preferences stable?","volume":"49","author":"S Andersen","year":"2008","journal-title":"International Economic Review"},{"key":"pcbi.1009217.ref024","unstructured":"von Neumann and Morgenstern. Theory of Games and Economic Behaviour. (Third Edition.). 1953."},{"key":"pcbi.1009217.ref025","article-title":"Did Ergodicity Economics and the Copenhagen Experiment Really Falsify Expected Utility Theory?","author":"A Goldstein","journal-title":"RESEARCHERSONE n.d"},{"key":"pcbi.1009217.ref026","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1016\/S0003-3472(80)80142-4","article-title":"An Empirical Demonstration of Risk-Sensitive Foraging Preferences","volume":"28","author":"T Caraco","year":"1980","journal-title":"Animal Behaviour"},{"key":"pcbi.1009217.ref027","article-title":"Risk-sensitivity and foraging groups","author":"T Caraco","year":"1981","journal-title":"Ecology"},{"key":"pcbi.1009217.ref028","doi-asserted-by":"crossref","first-page":"15788","DOI":"10.1073\/pnas.1308718110","article-title":"Thirst-dependent risk preferences in monkeys identify a primitive form of wealth","volume":"110","author":"H Yamada","year":"2013","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"pcbi.1009217.ref029","doi-asserted-by":"crossref","first-page":"e53978","DOI":"10.1371\/journal.pone.0053978","article-title":"State Dependent Valuation: The Effect of Deprivation on Risk Preferences","volume":"8","author":"DJ Levy","year":"2013","journal-title":"PLoS ONE"},{"key":"pcbi.1009217.ref030","doi-asserted-by":"crossref","first-page":"e11090","DOI":"10.1371\/journal.pone.0011090","article-title":"Metabolic State Alters Economic Decision Making under Risk in Humans","volume":"5","author":"M Symmonds","year":"2010","journal-title":"PLoS ONE"},{"key":"pcbi.1009217.ref031","doi-asserted-by":"crossref","first-page":"e0181112","DOI":"10.1371\/journal.pone.0181112","article-title":"Let the sunshine in? The effects of luminance on economic preferences, choice consistency and dominance violations","volume":"12","author":"PW Glimcher","year":"2017","journal-title":"PLOS ONE"},{"key":"pcbi.1009217.ref032","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1017\/S1930297500005532","article-title":"Effects of induced moods on economic choices","volume":"9","author":"SJ Stanton","year":"2014","journal-title":"Judgment and Decision Making"},{"key":"pcbi.1009217.ref033","first-page":"9","article-title":"Can We Infer Inter-Individual Differences in Risk-Taking From Behavioral Tasks?","author":"S Palminteri","year":"2018","journal-title":"Front Psychol"},{"key":"pcbi.1009217.ref034","doi-asserted-by":"crossref","first-page":"391","DOI":"10.3758\/s13423-014-0684-4","article-title":"Using Bayesian hierarchical parameter estimation to assess the generalizability of cognitive models of choice","volume":"22","author":"B Scheibehenne","year":"2015","journal-title":"Psychonomic Bulletin & Review"},{"key":"pcbi.1009217.ref035","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1038\/s41567-020-01106-x","article-title":"Economists\u2019 views on the ergodicity problem","volume":"16","author":"JN Doctor","year":"2020","journal-title":"Nat Phys"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1009217","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,9,21]],"date-time":"2021-09-21T00:00:00Z","timestamp":1632182400000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009217","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,8]],"date-time":"2023-01-08T22:39:27Z","timestamp":1673217567000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009217"}},"subtitle":[],"editor":[{"given":"Samuel J.","family":"Gershman","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2021,9,9]]},"references-count":35,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9,9]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1009217","relation":{"new_version":[{"id-type":"doi","id":"10.1371\/journal.pcbi.1009217","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,9]]}}}