# SFB 303 Discussion Paper No. A - 094

**Author**: Leininger, Wolfgang

**Title**: Strategic Equilibrium in Sequential Games

**Abstract**: The present analysis focuses on out of equilibrium moves (this statement requires that a certain equilibrium
has been proposed) that are compatible with another sequential equilibrium of the game and argues that if such
moves occur a prominent role should be assigned to beliefs that support the equilibria with which the given out
of equilibrium move is compatible. We define "credibility" of such moves in an inductive way and reject any
sequential equilibrium of a game as strategically not "stable" if at least one player can deviate from it ("to
another equilibrium") by a credible out of equilibrium move. A sequential equilibrium in which no player has
such a move is called a strategic equilibrium. The main result is that for any extensive form with generic pay-
offs strategic equilibrium exists.

The paper is organized as follows: Section II motivates our analysis heuristically
by looking at the backwards induction principle under perfect information. Section III develops a formal
definition of strategic equilibrium for games with perfect recall and provides an existence proof. The last section
contains a discussion of the relationship to other solution concepts; in particular to the notion of 'perfect
sequential equilibrium' proposed in Grossman and Perry (1985).

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: January 1987

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