SFB 303 Discussion Paper No. B - 228
Author: Nöldeke, Georg, and Larry Samuelson
Title: An Evolutionary Analysis of Backward and Forward Induction
Abstract: This paper examines the limiting behavior of a dynamic evolutionary process driven by stochastic learning
and rare mutations. The analysis is focused on extensive form games. We are especially interested in whether the
process yields outcomes that exhibit backward induction properties (such as subgame perfection) and forward
induction properties. We first examine what we call locally stable outcomes. Intuitively, our definition of local
stability requires that any strategy combination yielding a locally stable outcome is surrounded by learning
dynamics that at least eventually lead back to that outcome. Our interest in these outcomes not only has an
evolutionary motivation, as do static evolutionary stability concepts, but emerges from our dynamic model. If
our evolutionary process selects a unique outcome, this outcome must be locally stable. Locally stable outcomes
exhibit both backward and forward induction properties. In extensive form games in which each player moves at
most once along any path, every locally stable outcome is a subgame perfect equilibrium outcome. Furthermore,
every locally stable outcome must satisfy a forward induction property. In many games, locally stable outcomes
fail to exist. In such games the limiting distribution of the dynamic process will assign strictly positive
probability to multiple outcomes that are contained in locally stable components of absorbing sets of the learning
process. To address the question of whether the limiting distribution will satisfy backward and forward induction
properties in games where it does not generate a locally stable outcome, we turn to an analysis of the dynamic
process. We consider two simple classes of games, allowing us to deal with backward and forward induction one
at a time.
Keywords:
JEL-Classification-Number:
Creation-Date: November 1992
Unfortunately this paper is not available online. Please contact us to order a hardcopy.
SFB 303 Homepage
19.10.1999, Webmaster