{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:57:11Z","timestamp":1765040231356},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p> We analyze, from the point of view of quantum probability, statistical data from two interesting experiments, done by Shafir and Tversky [1, 2] in the domain of cognitive psychology. These are gambling experiments of Prisoner Dilemma type. They have important consequences for economics, especially for the justification of the Savage \"Sure Thing Principle\" [3] (implying that agents of the market behave rationally). Data from these experiments were astonishing, both from the viewpoint of cognitive psychology and economics and probability theory. Players behaved irrationally. Moreover, all attempts to generate these data by using classical Markov model were unsuccessful. In this note we show (by inventing a simple statistical test \u2014 generalized detailed balance condition) that these data are non-Kolmogorovian. We also show that it is neither quantum (i.e., it cannot be described by Dirac-von Neumann model). We proceed towards a quantum Markov model for these data. <\/jats:p>","DOI":"10.1142\/s123016120900027x","type":"journal-article","created":{"date-parts":[[2009,11,30]],"date-time":"2009-11-30T09:34:31Z","timestamp":1259573671000},"page":"371-385","source":"Crossref","is-referenced-by-count":35,"title":["Quantum Markov Model for Data from Shafir-Tversky Experiments in Cognitive Psychology"],"prefix":"10.1142","volume":"16","author":[{"given":"Luigi","family":"Accardi","sequence":"first","affiliation":[{"name":"Mathematical Center Vito Volterra, Department of Mathematics, University of Rome II, Italy"}]},{"given":"Andrei","family":"Khrennikov","sequence":"additional","affiliation":[{"name":"International Center for Mathematical Modeling in Physics and Cognitive Sciences, University of V\u00e4xj\u00f6, S-35195, Sweden"}]},{"given":"Masanori","family":"Ohya","sequence":"additional","affiliation":[{"name":"Department of Information Science, Tokyo University of Science, Noda-city, Chiba, 278-8510, Japan"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-0285(92)90015-T"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9280.1992.tb00678.x"},{"key":"rf3","volume-title":"The foundations of statistics","author":"Savage L. J.","year":"1954"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1023\/B:OPSY.0000047567.88377.74"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-2947-0_14"},{"key":"rf6","volume-title":"Interpretations of Probability","author":"Khrennikov A.Yu.","year":"1999"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/9789812793171_0001"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/34\/47\/304"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0303-2647(03)00041-8"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0479-3"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1023\/B:OPSY.0000047570.68941.9d"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.biosystems.2005.11.005"},{"key":"rf13","unstructured":"U.\u00a0Khrennikov, Quantum Bio-Informatics-2, eds. L.\u00a0Accardi, W.\u00a0Freudenberg and M.\u00a0Ohya (World Scientific, Singapore, 2008)\u00a0pp. 105\u2013118."},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/j.biosystems.2008.10.004"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-9593-1"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.09.061"},{"key":"rf17","first-page":"214","volume":"6","author":"Conte E.","journal-title":"Neuroquantology"},{"key":"rf18","first-page":"1","volume":"16","author":"Conte E.","journal-title":"Open Sys. Information Dyn."},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1177\/0022002788032003003"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1006\/obhd.1999.2846"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2006.01.003"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01078167"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/0370-1573(81)90070-3"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1007\/s002459900097"},{"key":"rf25","unstructured":"L.\u00a0Accardi, Quantum theory: reconsideration of foundations-3, American Institute of Physics, Ser. Conference Proceedings\u00a0810, eds. G.\u00a0Adenier, A. Yu.\u00a0Khrennikov and T.\u00a0Nieuwenhuizen (Melville, NY, 2006)\u00a0pp. 2\u201318."}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S123016120900027X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T16:22:18Z","timestamp":1565194938000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S123016120900027X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":25,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[2009,12]]}},"alternative-id":["10.1142\/S123016120900027X"],"URL":"https:\/\/doi.org\/10.1142\/s123016120900027x","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]}}}