TY  - GEN
AB  - 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.
DA  - 2011
KW  - Evolutionary game theory
KW  - best response dynamics
KW  - CURB sets
KW  - persistent retracts
KW  - asymptotic stability
KW  - Nash equilibrium refinements
KW  - learning
LA  - eng
PY  - 2011
SN  - 0931-6558
SP  - 28-
TI  - Refined best reply correspondence and dynamics
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29009529
Y2  - 2024-11-22T04:55:07
ER  -