working Paper
Refined best reply correspondence and dynamics
published
Dieter
Balkenborg
author
Josef
Hofbauer
author
Christoph
Kuzmics
author 235385640000-0003-2732-2838
10053
department
We call a correspondence, defined on the set of mixed strategy profiles, a generalized
best reply correspondence if it has a product structure, is upper
hemi-continuous, always includes a best reply to any mixed strategy profile,
and is convex- and closed-valued. For each generalized best reply correspondence
we define a generalized best reply dynamics as a differential inclusion based
on it. We call a face of the set of mixed strategy profiles a minimally asymptotically
stable face (MASF) if it is asymptotically stable under some such dynamics and
no subface of it is asymptotically stable under any such dynamics. The set of such
correspondences (and dynamics) is endowed with the partial order of point-wise
set-inclusion and, under a mild condition on the normal form of the game at hand,
forms a complete lattice with meets based on point-wise intersections. The refined
best reply correspondence is then defined as the smallest element of the set of all
generalized best reply correspondences. We ultimately find that every Kalai and
Samet's (1984) persistent retract, which coincide with Basu and Weibull's (1991)
CURB sets based, however, on the refined best reply correspondence, contains a
MASF. Conversely, every MASF must be a Voorneveld's (2004) prep set, again,
however, based on the refined best reply correspondence.
https://pub.uni-bielefeld.de/download/2900952/2900953/IMW_working_paper_451.pdf
application/x-downloadno
Center for Mathematical Economics2011
eng
Evolutionary game theorybest response dynamicsCURB setspersistent retractsasymptotic stabilityNash equilibrium refinementslearning
0931-6558urn:nbn:de:0070-pub-29009529
45128
https://pub.uni-bielefeld.de/record/2560231
D. Balkenborg, J. Hofbauer, and C. Kuzmics, <em>Refined best reply correspondence and dynamics</em>, Center For Mathematical Economics, Bielefeld, <strong>2011</strong>.
Balkenborg, D.; Hofbauer, J.; Kuzmics, C. (2011): Refined best reply correspondence and dynamics. Bielefeld: Center for Mathematical Economics.
Balkenborg D, Hofbauer J, Kuzmics C (2011) Working Papers. Institute of Mathematical Economics; 451.<br />Bielefeld: Center for Mathematical Economics.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Balkenborg, D., Hofbauer, J. & Kuzmics, C. (2011). <em>Refined best reply correspondence and dynamics</em> (Working Papers. Institute of Mathematical Economics). Bielefeld: Center for Mathematical Economics.</div>
Balkenborg, D., Hofbauer, J., & Kuzmics, C. (2011). <em>Refined best reply correspondence and dynamics</em> (Working Papers. Institute of Mathematical Economics, 451). Bielefeld: Center for Mathematical Economics.
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).
D. Balkenborg, J. Hofbauer, and C. Kuzmics, <em>Refined best reply correspondence and dynamics</em>, Working Papers. Institute of Mathematical Economics, vol. 451, Bielefeld: Center for Mathematical Economics, 2011.
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).
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Balkenborg, Dieter, Hofbauer, Josef, and Kuzmics, Christoph. 2011. <em>Refined best reply correspondence and dynamics</em>. Vol. 451. Working Papers. Institute of Mathematical Economics. Bielefeld: Center for Mathematical Economics.</div>
Balkenborg, D., Hofbauer, J., and Kuzmics, C. (2011). Refined best reply correspondence and dynamics. <em>Working Papers. Institute of Mathematical Economics</em>, 451, Bielefeld: Center for Mathematical Economics.
Balkenborg D, Hofbauer J, Kuzmics C (2011) <br /><em>Refined best reply correspondence and dynamics</em>. Working Papers. Institute of Mathematical Economics; 451.<br />Bielefeld: Center for Mathematical Economics.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Balkenborg, D., Hofbauer, J., & Kuzmics, C. (2011). <em>Refined best reply correspondence and dynamics</em> (Working Papers. Institute of Mathematical Economics, 451). Bielefeld: Center for Mathematical Economics.</div>
Balkenborg, D., Hofbauer, J., & Kuzmics, C., 2011. <em>Refined best reply correspondence and dynamics</em>, Working Papers. Institute of Mathematical Economics, no.451, Bielefeld: Center for Mathematical Economics.
Balkenborg, Dieter, Hofbauer, Josef, and Kuzmics, Christoph. <em>Refined best reply correspondence and dynamics</em>. Bielefeld: Center for Mathematical Economics, 2011. Working Papers. Institute of Mathematical Economics. 451.
Balkenborg D, Hofbauer J, Kuzmics C. <em>Refined best reply correspondence and dynamics</em>. Working Papers. Institute of Mathematical Economics. Vol 451. Bielefeld: Center for Mathematical Economics; 2011.
29009522016-02-11T13:31:41Z2018-07-24T13:00:59Z