{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:43:24Z","timestamp":1740109404133,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T00:00:00Z","timestamp":1715644800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T00:00:00Z","timestamp":1715644800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Game Theory"],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We examine infinite horizon decision problems with arbitrary bounded payoff functions in which the decision maker uses finitely additive behavioral strategies. Since we only assume that the payoff function is bounded, it is well-known that these behavioral strategies generally do not induce unambiguously defined expected payoffs. Consequently, it is not clear how to compare behavioral strategies and define optimality. We address this problem by finding conditions on the payoff function that guarantee an unambiguous expected payoff regardless of which behavioral strategy the decision maker uses. To this end, we systematically consider various alternatives proposed in the literature on how to define the finitely additive probability measure on the set of infinite plays induced by a behavioral strategy.<\/jats:p>","DOI":"10.1007\/s00182-024-00892-5","type":"journal-article","created":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T09:01:58Z","timestamp":1715677318000},"page":"695-723","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finitely additive behavioral strategies: when do they induce an unambiguous expected payoff?"],"prefix":"10.1007","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9599-4615","authenticated-orcid":false,"given":"J\u00e1nos","family":"Flesch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dries","family":"Vermeulen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anna","family":"Zseleva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,14]]},"reference":[{"key":"892_CR1","volume-title":"Infinite dimensional analysis","author":"D Aliprantis","year":"2005","unstructured":"Aliprantis D, Border KC (2005) Infinite dimensional analysis. Springer, Berlin"},{"issue":"5","key":"892_CR2","doi-asserted-by":"publisher","first-page":"1371","DOI":"10.3982\/ECTA7501","volume":"77","author":"NI Al-Najjar","year":"2009","unstructured":"Al-Najjar NI (2009) Decision makers as statisticians: diversity, ambiguity, and learning. Econometrica 77(5):1371\u20131401","journal-title":"Econometrica"},{"issue":"11","key":"892_CR3","doi-asserted-by":"publisher","first-page":"3725","DOI":"10.1257\/aer.104.11.3725","volume":"104","author":"N Al-Najjar","year":"2014","unstructured":"Al-Najjar N, Pomatto L, Sandroni A (2014) Claim validation. Am Econ Rev 104(11):3725\u20133736","journal-title":"Am Econ Rev"},{"key":"892_CR4","unstructured":"Bingham NH (2010) Finite additivity versus countable additivity. Electronic Journal for History of Probability and Statistics, vol 6, no 1"},{"key":"892_CR5","doi-asserted-by":"crossref","unstructured":"Capraro V, Scarsini M (2013) Existence of equilibria in countable games: An algebraic approach. Games and Economic Behavior, 79, issue C, 163-180","DOI":"10.1016\/j.geb.2013.01.010"},{"key":"892_CR6","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.geb.2022.05.011","volume":"135","author":"S Cerreia-Vioglio","year":"2022","unstructured":"Cerreia-Vioglio S, Maccheroni F, Schmeidler D (2022) Equilibria of nonatomic anonymous games. Games Econ Behav 135:110\u2013131","journal-title":"Games Econ Behav"},{"issue":"3","key":"892_CR7","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1214\/aop\/1176996660","volume":"2","author":"LE Dubins","year":"1974","unstructured":"Dubins LE (1974) On Lebesgue-like extensions of finitely additive measures. Annals Prob 2(3):456\u2013463","journal-title":"Annals Prob"},{"key":"892_CR8","unstructured":"Dubins LE, Savage LJ (2014) edited and updated by Sudderth, WD and Gilat, D, How to gamble if you must: inequalities for stochastic processes. Dover Publications, New York"},{"key":"892_CR9","volume-title":"Linear operators, Part I: general theory","author":"N Dunford","year":"1964","unstructured":"Dunford N, Schwartz JT (1964) Linear operators, Part I: general theory. Interscience Publishers, New York"},{"key":"892_CR10","volume-title":"The theory of probability (2 volumes)","author":"B de Finetti","year":"1975","unstructured":"de Finetti B (1975) The theory of probability (2 volumes). J. Wiley and Sons, Chichester"},{"key":"892_CR11","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1016\/j.geb.2016.10.014","volume":"102","author":"J Flesch","year":"2017","unstructured":"Flesch J, Vermeulen D, Zseleva A (2017) Zero-sum games with charges. Games Econ Behav 102:666\u2013686","journal-title":"Games Econ Behav"},{"issue":"3","key":"892_CR12","doi-asserted-by":"publisher","first-page":"810","DOI":"10.1017\/jpr.2019.47","volume":"56","author":"J Flesch","year":"2019","unstructured":"Flesch J, Vermeulen D, Zseleva A (2019) On the equivalence of mixed and behavior strategies in finitely additive decision problems. J Appl Prob 56(3):810\u2013829","journal-title":"J Appl Prob"},{"key":"892_CR13","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/978-3-319-20451-2_21","volume-title":"Readings in formal epistemology: sourcebook","author":"I Gilboa","year":"2016","unstructured":"Gilboa I, Marinacci M (2016) Ambiguity and the Bayesian paradigm. Readings in formal epistemology: sourcebook. Springer International Publishing, Cham, pp 385\u2013439"},{"key":"892_CR14","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.geb.2003.06.008","volume":"50","author":"JH Harris","year":"2005","unstructured":"Harris JH, Stinchcombe MB, Zame WR (2005) Nearly compact and continuous normal form games: characterizations and equilibrium existence. Games Econ Behav 50:208\u2013224","journal-title":"Games Econ Behav"},{"key":"892_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4","volume-title":"Classical Descriptive Set Theory","author":"AS Kechris","year":"1995","unstructured":"Kechris AS (1995) Classical Descriptive Set Theory. Springer-Verlag"},{"key":"892_CR16","doi-asserted-by":"publisher","first-page":"267","DOI":"10.4064\/fm-36-1-267-276","volume":"36","author":"J Lo\u015b","year":"1949","unstructured":"Lo\u015b J, Marczewski E (1949) Extensions of measure. Fundamenta Mathematicae, issue 36:267\u2013276","journal-title":"Fundamenta Mathematicae, issue"},{"key":"892_CR17","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/BF01240053","volume":"22","author":"A Maitra","year":"1993","unstructured":"Maitra A, Sudderth W (1993) Finitely additive and measurable stochastic games. Int J Game Theory 22:201\u2013223","journal-title":"Int J Game Theory"},{"key":"892_CR18","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/s001820050071","volume":"27","author":"A Maitra","year":"1998","unstructured":"Maitra A, Sudderth W (1998) Finitely additive stochastic games with Borel measurable payoffs. Int J Game Theory 27:257\u2013267","journal-title":"Int J Game Theory"},{"issue":"3","key":"892_CR19","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/BF01263274","volume":"26","author":"M Marinacci","year":"1997","unstructured":"Marinacci M (1997) Finitely additive and epsilon Nash equilibria. Int J Game Theory 26(3):315\u2013333","journal-title":"Int J Game Theory"},{"key":"892_CR20","unstructured":"Milchtaich I (2020) Best-response equilibrium: An equilibrium in finitely additive mixed strategies. Bar-Ilan University, Research Institute for Econometrics and Economic Theory, Working Paper"},{"issue":"3","key":"892_CR21","doi-asserted-by":"publisher","first-page":"1003","DOI":"10.1214\/14-AOS1212","volume":"42","author":"L Pomatto","year":"2014","unstructured":"Pomatto L, Al-Najjar N, Sandroni A (2014) Merging and testing opinions. Ann Stat 42(3):1003\u20131028","journal-title":"Ann Stat"},{"key":"892_CR22","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1214\/aop\/1176996133","volume":"4","author":"R Purves","year":"1976","unstructured":"Purves R, Sudderth W (1976) Some finitely additive probability. Ann Probability 4:259\u2013276","journal-title":"Ann Probability"},{"key":"892_CR23","volume-title":"Theory of charges: a study of finitely additive measures","author":"KPSB Rao","year":"1983","unstructured":"Rao KPSB, Rao B (1983) Theory of charges: a study of finitely additive measures. Academic Press, New York"},{"key":"892_CR24","volume-title":"The Foundations of Statistics","author":"LJ Savage","year":"1972","unstructured":"Savage LJ (1972) The Foundations of Statistics. Dover Publications, New York"},{"issue":"3","key":"892_CR25","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/s10959-007-0066-1","volume":"20","author":"O Schirokauer","year":"2007","unstructured":"Schirokauer O, Kadane JB (2007) Uniform distributions on the natural numbers. J Theoretical Prob 20(3):429\u2013441","journal-title":"J Theoretical Prob"},{"key":"892_CR26","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1287\/moor.2015.0717","volume":"41","author":"W Sudderth","year":"2016","unstructured":"Sudderth W (2016) Finitely additive dynamic programming. Math Oper Res 41:92\u2013108","journal-title":"Math Oper Res"}],"container-title":["International Journal of Game Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-024-00892-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00182-024-00892-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-024-00892-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T10:03:40Z","timestamp":1718964220000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00182-024-00892-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,14]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["892"],"URL":"https:\/\/doi.org\/10.1007\/s00182-024-00892-5","relation":{},"ISSN":["0020-7276","1432-1270"],"issn-type":[{"type":"print","value":"0020-7276"},{"type":"electronic","value":"1432-1270"}],"subject":[],"published":{"date-parts":[[2024,5,14]]},"assertion":[{"value":"6 March 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 May 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}