---
res:
bibo_abstract:
- "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.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Dieter
foaf_name: Balkenborg, Dieter
foaf_surname: Balkenborg
- foaf_Person:
foaf_givenName: Josef
foaf_name: Hofbauer, Josef
foaf_surname: Hofbauer
- foaf_Person:
foaf_givenName: Christoph
foaf_name: Kuzmics, Christoph
foaf_surname: Kuzmics
foaf_workInfoHomepage: http://www.librecat.org/personId=23538564
orcid: 0000-0003-2732-2838
bibo_volume: '451'
dct_date: 2011^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0931-6558
dct_language: eng
dct_publisher: Center for Mathematical Economics@
dct_subject:
- Evolutionary game theory
- best response dynamics
- CURB sets
- persistent retracts
- asymptotic stability
- Nash equilibrium refinements
- learning
dct_title: Refined best reply correspondence and dynamics@
...