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.
Creation-Date: November 1992
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