[{"author":[{"full_name":"Balkenborg, Dieter","first_name":"Dieter","last_name":"Balkenborg"},{"full_name":"Hofbauer, Josef","first_name":"Josef","last_name":"Hofbauer"},{"last_name":"Kuzmics","id":"23538564","first_name":"Christoph","orcid":"0000-0003-2732-2838","full_name":"Kuzmics, Christoph"}],"oa":1,"abstract":[{"lang":"eng","text":"We call a correspondence, defined on the set of mixed strategy profiles, a generalized\r\nbest reply correspondence if it has a product structure, is upper\r\nhemi-continuous, always includes a best reply to any mixed strategy profile,\r\nand is convex- and closed-valued. For each generalized best reply correspondence\r\nwe define a generalized best reply dynamics as a differential inclusion based\r\non it. We call a face of the set of mixed strategy profiles a minimally asymptotically\r\nstable face (MASF) if it is asymptotically stable under some such dynamics and\r\nno subface of it is asymptotically stable under any such dynamics. The set of such\r\ncorrespondences (and dynamics) is endowed with the partial order of point-wise\r\nset-inclusion and, under a mild condition on the normal form of the game at hand,\r\nforms a complete lattice with meets based on point-wise intersections. The refined\r\nbest reply correspondence is then defined as the smallest element of the set of all\r\ngeneralized best reply correspondences. We ultimately find that every Kalai and\r\nSamet's (1984) persistent retract, which coincide with Basu and Weibull's (1991)\r\nCURB sets based, however, on the refined best reply correspondence, contains a\r\nMASF. Conversely, every MASF must be a Voorneveld's (2004) prep set, again,\r\nhowever, based on the refined best reply correspondence."}],"keyword":["Evolutionary game theory","best response dynamics","CURB sets","persistent retracts","asymptotic stability","Nash equilibrium refinements","learning"],"date_created":"2016-02-11T13:31:41Z","volume":"451","_id":"2900952","urn":"urn:nbn:de:0070-pub-29009529","publication_identifier":{"issn":["0931-6558"]},"title":"Refined best reply correspondence and dynamics","file_date_updated":"2016-02-15T13:51:02Z","accept":"1","locked":"1","file":[{"access_level":"open_access","file_id":"2900953","creator":"weingarten","open_access":"1","content_type":"application/x-download","date_updated":"2016-02-15T13:51:02Z","date_created":"2016-02-11T13:28:17Z","file_size":"508486","success":"1","relation":"main_file","file_name":"IMW_working_paper_451.pdf"}],"year":"2011","edit_mode":"expert","first_author":"Balkenborg, Dieter","date_updated":"2018-07-24T13:00:59Z","related_material":{"record":[{"relation":"later_version","id":"2560231","status":"public"}]},"intvolume":" 451","ddc":["330"],"type":"working_paper","series_title":"Working Papers. Institute of Mathematical Economics","publisher":"Center for Mathematical Economics","page":"28","citation":{"aps":" D. Balkenborg, J. Hofbauer, and C. Kuzmics, Refined best reply correspondence and dynamics, Working Papers. Institute of Mathematical Economics (Center for Mathematical Economics, Bielefeld, 2011).","frontiers":"Balkenborg, D., Hofbauer, J., and Kuzmics, C. (2011). Refined best reply correspondence and dynamics. *Working Papers. Institute of Mathematical Economics*, 451, Bielefeld: Center for Mathematical Economics.","lncs":" Balkenborg, D., Hofbauer, J., Kuzmics, C.: Refined best reply correspondence and dynamics. Working Papers. Institute of Mathematical Economics, 451. Center for Mathematical Economics, Bielefeld (2011).","apa":"Balkenborg, D., Hofbauer, J., & Kuzmics, C. (2011). *Refined best reply correspondence and dynamics* (Working Papers. Institute of Mathematical Economics, 451). Bielefeld: Center for Mathematical Economics.","default":"Balkenborg D, Hofbauer J, Kuzmics C (2011) Working Papers. Institute of Mathematical Economics; 451.

Bielefeld: Center for Mathematical Economics.","ama":"Balkenborg D, Hofbauer J, Kuzmics C. *Refined best reply correspondence and dynamics*. Working Papers. Institute of Mathematical Economics. Vol 451. Bielefeld: Center for Mathematical Economics; 2011.","angewandte-chemie":"D. Balkenborg, J. Hofbauer, and C. Kuzmics, *Refined best reply correspondence and dynamics*, Center For Mathematical Economics, Bielefeld, **2011**.","wels":"Balkenborg, D.; Hofbauer, J.; Kuzmics, C. (2011): Refined best reply correspondence and dynamics. Bielefeld: Center for Mathematical Economics.","mla":"Balkenborg, Dieter, Hofbauer, Josef, and Kuzmics, Christoph. *Refined best reply correspondence and dynamics*. Bielefeld: Center for Mathematical Economics, 2011. Working Papers. Institute of Mathematical Economics. 451.","chicago":"Balkenborg, Dieter, Hofbauer, Josef, and Kuzmics, Christoph. 2011. *Refined best reply correspondence and dynamics*. Vol. 451. Working Papers. Institute of Mathematical Economics. Bielefeld: Center for Mathematical Economics.

","harvard1":"Balkenborg, D., Hofbauer, J., & Kuzmics, C., 2011. *Refined best reply correspondence and dynamics*, Working Papers. Institute of Mathematical Economics, no.451, Bielefeld: Center for Mathematical Economics.","dgps":"Balkenborg, D., Hofbauer, J. & Kuzmics, C. (2011). *Refined best reply correspondence and dynamics* (Working Papers. Institute of Mathematical Economics). Bielefeld: Center for Mathematical Economics.

","ieee":" D. Balkenborg, J. Hofbauer, and C. Kuzmics, *Refined best reply correspondence and dynamics*, Working Papers. Institute of Mathematical Economics, vol. 451, Bielefeld: Center for Mathematical Economics, 2011.","apa_indent":"Balkenborg, D., Hofbauer, J., & Kuzmics, C. (2011). *Refined best reply correspondence and dynamics* (Working Papers. Institute of Mathematical Economics, 451). Bielefeld: Center for Mathematical Economics.

","bio1":"Balkenborg D, Hofbauer J, Kuzmics C (2011)

*Refined best reply correspondence and dynamics*. Working Papers. Institute of Mathematical Economics; 451.

Bielefeld: Center for Mathematical Economics."},"publication_status":"published","jel":["C62","C72","C73"],"place":"Bielefeld","status":"public","department":[{"_id":"10053"}],"language":[{"iso":"eng"}]}]