SFB 303 Discussion Paper No. B - 321
Author: Cressman, R., and K.H. Schlag
Title: Dynamic Stability in perturbed Games
Abstract: The effect that exogenous mistakes, made by players choosing their
strategies, have on the dynamic stability for the replicator dynamic is
analyzed for both asymmetric and symmetric normal form games. Through these
perturbed games, the dynamic solution concept of limit asymptotic stability
is motivated by insisting that such solutions be asymptotically stable for
all sufficiently small perturbations (a robustness property). Limit
asymptotic stability is then a refinement of the Nash equilibrium. For
asymmetric normal form games, it is shown that a strategy pair is limit
asymptotically stable if and only if it is a pure strategy pair that weakly
dominates alternative best replies. For symmetric normal form games, all
evolutionarily stable strategies (ESS's), whether pure or mixed, are limit
asymptotically stable. Here, conditions are established for limit asymptotic
stability of completely mixed (i.e. interior) strategies as well as
strategies on the boundary. Consistency with solutions found by backwards
and/or forwards induction is shown for elementary extensive form games.
Limit asymptotically stable sets are introduced that generalize other
set-values solutions concepts such as the "strict equilibrium set" and the
"ES set" for asymmetric and symmetric normal form games respectively.
Keywords:
JEL-Classification-Number:
Creation-Date: July 1995
URL: ../1995/b/bonnsfb321.ps
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