SFB 303 Discussion Paper No. B-347

Author: Schlag, Karl H., and Ross Cressman

Title: The Dynamic (In)Stability of Backwards Induction

Abstract: The analysis of the replicator dynamic in generic prfect information games yields the following results. In the long run, players play a Nash equlilbrium provided that initially all strategies are present. There is at most one "stable" component ( formally, an interior asymptotically stable set ), play in this component will follow the backwards induction path. Existence of such a component is guraranteed in games with at most three consecutive decisions nodes. An example of a "longer"game is provided whre some trajectories starting close to the backwards induction component lead away and never come back.

Keywords: perfect informatin, extensiv-form game, Centipede Game, backwards induction, replicator dynamics, interior asymptotic stability

JEL-Classification-Number: C 72, C79

Creation-Date: May 1995
URL: ../1995/b/bonnsfb347.ps

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