{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T16:44:45Z","timestamp":1769877885461,"version":"3.49.0"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2011,10]]},"DOI":"10.1007\/s00186-010-0342-1","type":"journal-article","created":{"date-parts":[[2011,1,3]],"date-time":"2011-01-03T12:36:28Z","timestamp":1294058188000},"page":"147-161","source":"Crossref","is-referenced-by-count":6,"title":["On evolutionary ray-projection dynamics"],"prefix":"10.1007","volume":"74","author":[{"given":"Reinoud","family":"Joosten","sequence":"first","affiliation":[]},{"given":"Berend","family":"Roorda","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,1,4]]},"reference":[{"key":"342_CR1","doi-asserted-by":"crossref","first-page":"82","DOI":"10.2307\/1907779","volume":"27","author":"KJ Arrow","year":"1959","unstructured":"Arrow KJ, Block HD, Hurwicz L (1959) On the stability of the competitive equilibrium II. Econometrica 27: 82\u2013109","journal-title":"Econometrica"},{"key":"342_CR2","doi-asserted-by":"crossref","first-page":"522","DOI":"10.2307\/1907515","volume":"26","author":"KJ Arrow","year":"1958","unstructured":"Arrow KJ, Hurwicz L (1958) On the stability of the competitive equilibrium I. Econometrica 26: 522\u2013552","journal-title":"Econometrica"},{"key":"342_CR3","doi-asserted-by":"crossref","first-page":"38","DOI":"10.2307\/2525407","volume":"1","author":"KJ Arrow","year":"1960","unstructured":"Arrow KJ, Hurwicz L (1960a) Competitive stability under weak gross substitutability: the \u201cEuclidean distance\u201d approach. Int Econ Rev 1: 38\u201349","journal-title":"Int Econ Rev"},{"key":"342_CR4","doi-asserted-by":"crossref","first-page":"640","DOI":"10.2307\/1910137","volume":"28","author":"KJ Arrow","year":"1960","unstructured":"Arrow KJ, Hurwicz L (1960b) Some remarks on the equilibria of economic systems. Econometrica 28: 640\u2013646","journal-title":"Econometrica"},{"key":"342_CR5","first-page":"155","volume-title":"The rational foundations of economic behavior","author":"J Bj\u00f6rnerstedt","year":"1996","unstructured":"Bj\u00f6rnerstedt J, Weibull J (1996) Nash equilibrium and evolution by imitation. In: Arrow KJ (eds) The rational foundations of economic behavior. MacMillan, London, pp 155\u2013171"},{"key":"342_CR6","first-page":"374","volume-title":"Activity analysis of production and allocation","author":"GW Brown","year":"1951","unstructured":"Brown GW (1951) Iterative solutions of games by fictitious play. In: Koopmans T (eds) Activity analysis of production and allocation. Wiley, NY, pp 374\u2013376"},{"key":"342_CR7","first-page":"73","volume-title":"Solutions of games by differential equations. Annals of mathematics studies, vol 24","author":"GW Brown","year":"1950","unstructured":"Brown GW, von Neumann J (1950) Solutions of games by differential equations. Annals of mathematics studies, vol 24. Princeton University Press, Princeton, pp 73\u201379"},{"key":"342_CR8","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0022-0531(92)90043-H","volume":"57","author":"A Cabrales","year":"1992","unstructured":"Cabrales A, Sobel J (1992) On the limit points of discrete selection dynamics. J Econ Theory 57: 407\u2013419","journal-title":"J Econ Theory"},{"key":"342_CR9","doi-asserted-by":"crossref","first-page":"637","DOI":"10.2307\/2938222","volume":"59","author":"D Friedman","year":"1991","unstructured":"Friedman D (1991) Evolutionary games in economics. Econometrica 59: 637\u2013666","journal-title":"Econometrica"},{"key":"342_CR10","volume-title":"The theory of learning in games","author":"D Fudenberg","year":"1998","unstructured":"Fudenberg D, Levine DK (1998) The theory of learning in games. MIT Press, Cambridge"},{"key":"342_CR11","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1556\/Select.1.2000.1-3.8","volume":"1","author":"J Hofbauer","year":"2000","unstructured":"Hofbauer J (2000) From Nash and Brown to Maynard Smith: equilibria, dynamics, and ESS. Selection 1: 81\u201388","journal-title":"Selection"},{"key":"342_CR12","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1016\/j.jet.2009.01.007","volume":"144","author":"J Hofbauer","year":"2009","unstructured":"Hofbauer J, Sandholm WH (2009) Stable games and their dynamics. J Econ Theory 144: 1665\u20131693","journal-title":"J Econ Theory"},{"key":"342_CR13","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":"342_CR14","volume-title":"The theory of evolution and dynamical systems","author":"J Hofbauer","year":"1988","unstructured":"Hofbauer J, Sigmund K (1988) The theory of evolution and dynamical systems. Cambridge University Press, Cambridge"},{"key":"342_CR15","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1006\/game.1997.0636","volume":"29","author":"E Hopkins","year":"1999","unstructured":"Hopkins E (1999) A note on best response dynamics. Games Econ Behav 29: 138\u2013150","journal-title":"Games Econ Behav"},{"key":"342_CR16","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/BF01193636","volume":"6","author":"R Joosten","year":"1996","unstructured":"Joosten R (1996) Deterministic evolutionary dynamics: a unifying approach. J Evol Econ 6: 313\u2013324","journal-title":"J Evol Econ"},{"key":"342_CR17","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/s00191-006-0037-1","volume":"16","author":"R Joosten","year":"2006","unstructured":"Joosten R (2006) Walras and Darwin: an odd couple?. J Evolut Econ 16: 561\u2013573","journal-title":"J Evolut Econ"},{"key":"342_CR18","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/j.geb.2008.02.002","volume":"64","author":"R Lahkar","year":"2008","unstructured":"Lahkar R, Sandholm WH (2008) The projection dynamic and the geometry of population games. Games Econ Behav 64: 565\u2013590","journal-title":"Games Econ Behav"},{"key":"342_CR19","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0022-0531(92)90040-O","volume":"57","author":"A Matsui","year":"1992","unstructured":"Matsui A (1992) Best-response dynamics and socially stable strategies. J Econ Theory 57: 343\u2013362","journal-title":"J Econ Theory"},{"key":"342_CR20","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/S0899-8256(02)00014-3","volume":"41","author":"LG Mattson","year":"2002","unstructured":"Mattson LG, Weibull JW (2002) Probabilistic choice and procedural bounded rationality. Games Econ Behav 41: 61\u201378","journal-title":"Games Econ Behav"},{"key":"342_CR21","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":"342_CR22","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1038\/246015a0","volume":"246","author":"J Maynard Smith","year":"1973","unstructured":"Maynard Smith J, Price GA (1973) The logic of animal conflict. Nature 246: 15\u201318","journal-title":"Nature"},{"key":"342_CR23","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/BF01753708","volume":"19","author":"JH Nachbar","year":"1990","unstructured":"Nachbar JH (1990) \u2018Evolutionary\u2019 selection dynamics in games: convergence and limit properties. Int J Game Theory 19: 59\u201389","journal-title":"Int J Game Theory"},{"key":"342_CR24","doi-asserted-by":"crossref","first-page":"635","DOI":"10.2307\/1909319","volume":"30","author":"T Negishi","year":"1962","unstructured":"Negishi T (1962) The stability of a competitive economy: a survey article. Econometrica 30: 635\u2013669","journal-title":"Econometrica"},{"key":"342_CR25","doi-asserted-by":"crossref","first-page":"654","DOI":"10.2307\/1909356","volume":"27","author":"H Nikaid\u00f4","year":"1959","unstructured":"Nikaid\u00f4 H (1959) Stability of equilibrium by the Brown-von Neumann differential equation. Econometrica 27: 654\u2013671","journal-title":"Econometrica"},{"key":"342_CR26","doi-asserted-by":"crossref","first-page":"50","DOI":"10.2307\/2525408","volume":"1","author":"H Nikaid\u00f4","year":"1960","unstructured":"Nikaid\u00f4 H, Uzawa H (1960) Stability and non-negativity in a Walrasian t\u00e2tonnement process. Int Econ Rev 1: 50\u201359","journal-title":"Int Econ Rev"},{"key":"342_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0392-3","volume-title":"Differential equations and dynamical systems","author":"L Perko","year":"1991","unstructured":"Perko L (1991) Differential equations and dynamical systems. Springer, Berlin"},{"key":"342_CR28","doi-asserted-by":"crossref","first-page":"1371","DOI":"10.2307\/2171774","volume":"63","author":"K Ritzberger","year":"1995","unstructured":"Ritzberger K, Weibull J (1995) Evolutionary selection in normal form games. Econometrica 63: 1371\u20131399","journal-title":"Econometrica"},{"key":"342_CR29","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/BF00536300","volume":"17","author":"J Rosenm\u00fcller","year":"1971","unstructured":"Rosenm\u00fcller J (1971) \u00dcber die Periodizit\u00e4tseigenschaften spieltheoretischer Lernprozesse. Zeitschrift f\u00fcr Warscheinlichkeitstheorie und verwandte Gebiete 17: 259\u2013308","journal-title":"Zeitschrift f\u00fcr Warscheinlichkeitstheorie und verwandte Gebiete"},{"key":"342_CR30","doi-asserted-by":"crossref","first-page":"61","DOI":"10.2307\/2548836","volume":"5","author":"P Samuelson","year":"1938","unstructured":"Samuelson P (1938) A note on the pure theory of consumer behavior. Economica 5: 61\u201371","journal-title":"Economica"},{"key":"342_CR31","doi-asserted-by":"crossref","first-page":"97","DOI":"10.2307\/1906872","volume":"9","author":"P Samuelson","year":"1941","unstructured":"Samuelson P (1941) The stability of equilibrium: comparative statics and dynamics. Econometrica 9: 97\u2013120","journal-title":"Econometrica"},{"key":"342_CR32","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.jet.2005.02.003","volume":"124","author":"WH Sandholm","year":"2005","unstructured":"Sandholm WH (2005) Excess payoff dynamics and other well-behaved evolutionary dynamics. J Econ Theory 124: 149\u2013170","journal-title":"J Econ Theory"},{"key":"342_CR33","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1006\/game.1997.0613","volume":"23","author":"R Sethi","year":"1998","unstructured":"Sethi R (1998) Strategy-specific barriers to learning and non-monotonic selection dynamics. Games Econ Behav 23: 284\u2013304","journal-title":"Games Econ Behav"},{"key":"342_CR34","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1006\/game.1993.1025","volume":"5","author":"J Swinkels","year":"1993","unstructured":"Swinkels J (1993) Adjustment dynamics and rational play in games. Games Econ Behav 5: 455\u2013484","journal-title":"Games Econ Behav"},{"key":"342_CR35","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0025-5564(78)90077-9","volume":"40","author":"PD Taylor","year":"1978","unstructured":"Taylor PD, Jonker LB (1978) Evolutionarily stable strategies and game dynamics. Math Biosci 40: 145\u2013156","journal-title":"Math Biosci"},{"key":"342_CR36","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1016\/j.geb.2009.01.003","volume":"67","author":"E Tsakas","year":"2009","unstructured":"Tsakas E, Voorneveld M (2009) The target projection dynamic. Games Econ Behav 67: 708\u2013719","journal-title":"Games Econ Behav"},{"key":"342_CR37","doi-asserted-by":"crossref","first-page":"617","DOI":"10.2307\/1911808","volume":"29","author":"H Uzawa","year":"1961","unstructured":"Uzawa H (1961) The stability of dynamic processes. Econometrica 29: 617\u2013631","journal-title":"Econometrica"},{"key":"342_CR38","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-58242-4","volume-title":"Stability and perfection of Nash equilibria","author":"EEC Van Damme","year":"1991","unstructured":"Van Damme EEC (1991) Stability and perfection of Nash equilibria. Springer, Berlin"},{"key":"342_CR39","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/s00182-005-0003-4","volume":"34","author":"M Voorneveld","year":"2006","unstructured":"Voorneveld M (2006) Probabilistic choice in games: properties of Rosenthal\u2019s t-solutions. Int J Game Theory 34: 105\u2013121","journal-title":"Int J Game Theory"},{"key":"342_CR40","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0022-5193(81)90311-8","volume":"89","author":"EC Zeeman","year":"1981","unstructured":"Zeeman EC (1981) Dynamics of the evolution of animal conflicts. J Theor Biol 89: 249\u2013270","journal-title":"J Theor Biol"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.springerlink.com\/index\/pdf\/10.1007\/s00186-010-0342-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,19]],"date-time":"2017-06-19T17:57:03Z","timestamp":1497895023000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00186-010-0342-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,4]]},"references-count":40,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,10]]}},"alternative-id":["342"],"URL":"https:\/\/doi.org\/10.1007\/s00186-010-0342-1","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"value":"1432-2994","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1,4]]}}}