Arbeitspapier

On the stability of CSS under the replicator dynamic

This paper considers a two-player game with a one-dimensional continuous strategy. We study the asymptotic stability of equilibria under the replicator dynamic when the support of the initial population is an interval. We find that, under strategic complementarities, Continuously Stable Strategy (CSS) have the desired convergence properties using an iterated dominance argument. For general games, however, CSS can be unstable even for populations that have a continuous support. We present a sufficient condition for convergence based on elimination of iteratively dominated strategies. This condition is more restrictive than CSS in general but equivalent in the case of strategic complementarities. Finally, we offer several economic applications of our results.

Language: Englisch

Bibliographic citation: Series: Working Papers ; No. 436

Classification: Wirtschaft
Stochastic and Dynamic Games; Evolutionary Games; Repeated Games

Subject: Continuously Stable Strategy (CSS)
Evolutionary stability
Evolutionäre Spieltheorie
Gleichgewichtsstabilität
Theorie

Event: Geistige Schöpfung

(who): Louge, Fernando

Event: Veröffentlichung

(who): Bielefeld University, Institute of Mathematical Economics (IMW)

(where): Bielefeld

(when): 2010

Handle: http://hdl.handle.net/10419/43757

URN: urn:nbn:de:hbz:361-17302

Last update: 10.03.2025, 11:45 AM CET

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Object type

Arbeitspapier

Associated

Louge, Fernando
Bielefeld University, Institute of Mathematical Economics (IMW)

Time of origin

2010