{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T09:23:22Z","timestamp":1768469002861,"version":"3.49.0"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,9,22]],"date-time":"2015-09-22T00:00:00Z","timestamp":1442880000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Grant-in-Aid for JSPS Fellows","award":["13J05358"],"award-info":[{"award-number":["13J05358"]}]},{"name":"JSPS KAKENHI","award":["25118006"],"award-info":[{"award-number":["25118006"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Dyn Games Appl"],"published-print":{"date-parts":[[2017,3]]},"DOI":"10.1007\/s13235-015-0170-2","type":"journal-article","created":{"date-parts":[[2015,9,22]],"date-time":"2015-09-22T06:42:33Z","timestamp":1442904153000},"page":"93-111","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Fixation Probabilities of Strategies for Bimatrix Games in Finite Populations"],"prefix":"10.1007","volume":"7","author":[{"given":"Takuya","family":"Sekiguchi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hisashi","family":"Ohtsuki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,9,22]]},"reference":[{"key":"170_CR1","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/j.jtbi.2009.02.010","volume":"258","author":"T Antal","year":"2009","unstructured":"Antal T, Traulsen A, Ohtsuki H, Tarnita CE, Nowak MA (2009) Mutation-selection equilibrium in games with multiple strategies. J Theor Biol 258:614\u2013622","journal-title":"J Theor Biol"},{"key":"170_CR2","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1177\/0022002797041003003","volume":"41","author":"G Bornstein","year":"1997","unstructured":"Bornstein G, Budescu D, Zamir S (1997) Cooperation in intergroup, N-person, and two-person games of chicken. J Conflict Resolut 41:384\u2013406","journal-title":"J Conflict Resolut"},{"key":"170_CR3","unstructured":"B\u00f8e T (1997) Evolutionary game theory and the battle of sexes. Chr. Michelsen Institute working paper"},{"key":"170_CR4","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1177\/1043463108089544","volume":"20","author":"YS Chiang","year":"2008","unstructured":"Chiang YS (2008) A path toward fairness: preferential association and the evolution of strategies in the ultimatum game. Ration Soc 20:173\u2013201","journal-title":"Ration Soc"},{"key":"170_CR5","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/2884.001.0001","volume-title":"Evolutionary dynamics and extensive form games","author":"R Cressman","year":"2003","unstructured":"Cressman R (2003) Evolutionary dynamics and extensive form games. MIT Press, Cambridge"},{"key":"170_CR6","unstructured":"Camerer CF (2003) Behavioral game theory: experiments on strategic interaction. Princeton University Press, Princeton"},{"key":"170_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1098\/rspb.2013.2439","volume":"281","author":"P Forber","year":"2014","unstructured":"Forber P, Smead R (2014) The evolution of fairness through spite. Proc Biol Sci 281:1\u20138","journal-title":"Proc Biol Sci"},{"key":"170_CR8","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/S0899-8256(05)80017-X","volume":"8","author":"J Gale","year":"1995","unstructured":"Gale J, Binmore K, Samuelson L (1995) Learning to be imperfect: the ultimatum game. Games Econ Behav 8:56\u201390","journal-title":"Games Econ Behav"},{"key":"170_CR9","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0040-5809(91)90028-E","volume":"39","author":"A Gaunersdorfer","year":"1991","unstructured":"Gaunersdorfer A, Hofbauer J, Sigmund K (1991) On the dynamics of asymmetric games. Theor Popul Biol 39:345\u2013357","journal-title":"Theor Popul Biol"},{"key":"170_CR10","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/0167-2681(82)90011-7","volume":"3","author":"W G\u00fcth","year":"1982","unstructured":"G\u00fcth W, Schmittberger R, Schwarze B (1982) An experimental analysis of ultimatum bargaining. J Econ Behav Organ 3:367\u2013388","journal-title":"J Econ Behav Organ"},{"key":"170_CR11","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0003-3472(81)80166-2","volume":"29","author":"P Hammerstein","year":"1981","unstructured":"Hammerstein P (1981) The role of asymmetries in animal contests. Anim Behav 29:193\u2013205","journal-title":"Anim Behav"},{"key":"170_CR12","volume-title":"A general theory of equilibrium selection in games","author":"JC Harsanyi","year":"1988","unstructured":"Harsanyi JC, Selten R (1988) A general theory of equilibrium selection in games. MIT Press, Cambridge"},{"key":"170_CR13","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1126\/science.1141588","volume":"316","author":"C Hauert","year":"2007","unstructured":"Hauert C, Traulsen A, Brandt H, Nowak MA, Sigmund K (2007) Via freedom to coercion: the emergence of costly punishment. Science 316:1905\u20131907","journal-title":"Science"},{"key":"170_CR14","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1162\/biot.2008.3.2.114","volume":"3","author":"C Hauert","year":"2008","unstructured":"Hauert C, Traulsen A, Brandt H, Nowak MA, Sigmund K (2008) Public goods with punishment and abstaining in finite and infinite populations. Biol Theory 3:114\u2013122","journal-title":"Biol Theory"},{"key":"170_CR15","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1007\/BF02409754","volume":"34","author":"J Hofbauer","year":"1996","unstructured":"Hofbauer J (1996) Evolutionary dynamics for bimatrix games: a hamiltonian system? J Math Biol 34:675\u2013688","journal-title":"J Math Biol"},{"key":"170_CR16","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/0022-5193(79)90058-4","volume":"81","author":"J Hofbauer","year":"1979","unstructured":"Hofbauer J, Schuster P, Sigmund K (1979) A note on evolutionary stable strategies and game dynamics. J Theor Biol 81:609\u2013612","journal-title":"J Theor Biol"},{"key":"170_CR17","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139173179","volume-title":"Evolutionary games and population dynamics","author":"J Hofbauer","year":"1998","unstructured":"Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge University Press, Cambridge"},{"key":"170_CR18","doi-asserted-by":"crossref","first-page":"10797","DOI":"10.1073\/pnas.0502589102","volume":"102","author":"LA Imhof","year":"2006","unstructured":"Imhof LA, Fudenberg D, Nowak MA (2006) Evolutionary cycles of cooperation and defection. Proc Natl Acad Sci USA 102:10797\u201310800","journal-title":"Proc Natl Acad Sci USA"},{"key":"170_CR19","doi-asserted-by":"crossref","first-page":"29","DOI":"10.2307\/2951777","volume":"61","author":"M Kandori","year":"1993","unstructured":"Kandori M, Mailath GJ, Rob R (1993) Learning, mutation, and long run equilibria in games. Econometrica 61:29\u201356","journal-title":"Econometrica"},{"key":"170_CR20","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1098\/rspb.2008.1546","volume":"276","author":"S Kurokawa","year":"2009","unstructured":"Kurokawa S, Ihara Y (2009) Emergence of cooperation in public goods games. Proc R Soc B Biol Sci 276:1379\u20131384","journal-title":"Proc R Soc B Biol Sci"},{"key":"170_CR21","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.tpb.2009.03.006","volume":"76","author":"L Lehmann","year":"2009","unstructured":"Lehmann L, Rousset F (2009) Perturbation expansions of multilocus fixation probabilities for frequency-dependent selection with applications to the Hill-Robertson effect and to the joint evolution of helping and punishment. Theor Popul Biol 76:35\u201351","journal-title":"Theor Popul Biol"},{"key":"170_CR22","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511806292","volume-title":"Evolution and the theory of games","author":"J Maynard-Smith","year":"1982","unstructured":"Maynard-Smith J (1982) Evolution and the theory of games. Cambridge University Press, Cambridge"},{"key":"170_CR23","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1038\/246015a0","volume":"246","author":"J Maynard-Smith","year":"1973","unstructured":"Maynard-Smith J, Price GR (1973) The logic of animal conflicts. Nature 246:15\u201318","journal-title":"Nature"},{"key":"170_CR24","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctvjghw98","volume-title":"Evolutionary dynamics: exploring the equations of life","author":"MA Nowak","year":"2006","unstructured":"Nowak MA (2006) Evolutionary dynamics: exploring the equations of life. Harvard University Press, Cambridge"},{"key":"170_CR25","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1126\/science.289.5485.1773","volume":"289","author":"MA Nowak","year":"2000","unstructured":"Nowak MA, Page K, Sigmund K (2000) Fairness versus reason in the ultimatum game. Science 289:1773\u20131775","journal-title":"Science"},{"key":"170_CR26","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1038\/nature02414","volume":"428","author":"MA Nowak","year":"2004","unstructured":"Nowak MA, Sasaki A, Taylor C, Fudenberg D (2004) Emergence of cooperation and evolutionary stability in finite populations. Nature 428:646\u2013650","journal-title":"Nature"},{"key":"170_CR27","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.jtbi.2010.01.016","volume":"264","author":"H Ohtsuki","year":"2010","unstructured":"Ohtsuki H (2010) Stochastic evolutionary dynamics of bimatrix games. J Theor Biol 264:136\u2013142","journal-title":"J Theor Biol"},{"key":"170_CR28","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.1098\/rspb.2000.1266","volume":"267","author":"KM Page","year":"2000","unstructured":"Page KM, Nowak MA, Sigmund K (2000) The spatial ultimatum game. Proc R Soc B Biol Sci 267:2177\u20132182","journal-title":"Proc R Soc B Biol Sci"},{"key":"170_CR29","doi-asserted-by":"crossref","first-page":"2581","DOI":"10.1073\/pnas.1214167110","volume":"110","author":"DG Rand","year":"2013","unstructured":"Rand DG, Tarnita CE, Ohtsuki H, Nowak MA (2013) Evolution of fairness in the one-shot anonymous ultimatum game. Proc Natl Acad Sci USA 110:2581\u20132586","journal-title":"Proc Natl Acad Sci USA"},{"key":"170_CR30","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1006\/jtbi.2003.3210","volume":"221","author":"F Rousset","year":"2003","unstructured":"Rousset F (2003) A minimal derivation of convergence stability measures. J Theor Biol 221:665\u2013668","journal-title":"J Theor Biol"},{"key":"170_CR31","doi-asserted-by":"crossref","DOI":"10.1515\/9781400847242","volume-title":"Genetic structure and selection in subdivided populations","author":"F Rousset","year":"2004","unstructured":"Rousset F (2004) Genetic structure and selection in subdivided populations. Princeton University Press, Princeton"},{"key":"170_CR32","volume-title":"Evolutionary games and equilibrium selection","author":"L Samuelson","year":"1997","unstructured":"Samuelson L (1997) Evolutionary games and equilibrium selection. MIT Press, Cambridge"},{"key":"170_CR33","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0022-0531(92)90041-F","volume":"57","author":"L Samuelson","year":"1992","unstructured":"Samuelson L, Zhang J (1992) Evolutionary stability in asymmetric games. J Econ Theory 57:363\u2013391","journal-title":"J Econ Theory"},{"key":"170_CR34","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/BF01766400","volume":"4","author":"R Seleten","year":"1975","unstructured":"Seleten R (1975) Reexamination of the perfectness concept for equilibrium points in extensive games. Int J Game Theory 4:25\u201355","journal-title":"Int J Game Theory"},{"key":"170_CR35","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BF00131770","volume":"9","author":"R Selten","year":"1978","unstructured":"Selten R (1978) The chain-store paradox. Theory Decis 9:127\u2013159","journal-title":"Theory Decis"},{"key":"170_CR36","doi-asserted-by":"crossref","first-page":"2886","DOI":"10.1016\/j.physa.2013.03.004","volume":"392","author":"T Sekiguchi","year":"2013","unstructured":"Sekiguchi T (2013) General conditions for strategy abundance through a self-referential mechanism under weak selection. Phys A 392:2886\u20132892","journal-title":"Phys A"},{"key":"170_CR37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00182-011-0271-0","volume":"41","author":"Y Shirata","year":"2012","unstructured":"Shirata Y (2012) The evolution of fairness under an assortative matching rule in the ultimatum game. Int J Game Theory 41:1\u201321","journal-title":"Int J Game Theory"},{"key":"170_CR38","doi-asserted-by":"crossref","unstructured":"Taylor PD, Jonker LB (1978) Evolutionarily stable strategies and game dynamics. Math Biosci 40:145\u2013156","DOI":"10.1016\/0025-5564(78)90077-9"},{"key":"170_CR39","volume-title":"Coalescent theory: an introduction","author":"J Wakeley","year":"2009","unstructured":"Wakeley J (2009) Coalescent theory: an introduction. Roberts and Company Publishers, Colorado"},{"key":"170_CR40","volume-title":"Evolutionary game theory","author":"J Weibull","year":"1995","unstructured":"Weibull J (1995) Evolutionary game theory. MIT Press, Cambridge"},{"key":"170_CR41","doi-asserted-by":"crossref","first-page":"2345","DOI":"10.1098\/rspb.2004.2862","volume":"271","author":"G Wild","year":"2004","unstructured":"Wild G, Taylor PD (2004) Fitness and evolutionary stability in game theoretic models of finite populations. Proc R Soc Lond B Biol Sci 271:2345\u20132349","journal-title":"Proc R Soc Lond B Biol Sci"},{"key":"170_CR42","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/s10614-014-9435-x","volume":"45","author":"Y Zhang","year":"2015","unstructured":"Zhang Y, Gao X (2015) Stochastic evolutionary selection in heterogeneous populations for asymmetric games. Comput Econ 45:501\u2013515","journal-title":"Comput Econ"}],"container-title":["Dynamic Games and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-015-0170-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13235-015-0170-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-015-0170-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-015-0170-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,22]],"date-time":"2022-05-22T03:28:05Z","timestamp":1653190085000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13235-015-0170-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,22]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["170"],"URL":"https:\/\/doi.org\/10.1007\/s13235-015-0170-2","relation":{},"ISSN":["2153-0785","2153-0793"],"issn-type":[{"value":"2153-0785","type":"print"},{"value":"2153-0793","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9,22]]}}}