Matching Best Replies in the Centipede Game

Abstract

By applying their Best-Reply Matching (BRM) equilibrium concept to the well known finite centipede game, Droste, Kosfeld & Voorneveld DKV (2003) showed that players continue the game with large probability. In this paper we build on their work by first showing that the BRM equilibria differ whether one works with the normal or with the reduced normal form of a game. This leads us to propose a natural modification to DKV's criterion, which leads to the same set of equilibria regardless of the chosen representation of a game (normal form and reduced normal form). Finally we show that the new concept, in the centipede game, gives rise a larger set of behaviors, which includes the Subgame Perfect Nash equilibrium but also a bounded rational behavior that incites the player to never stop the game with a probability larger than 1/2.

Keywords: Best-reply matching, centipede game, reduced normal form, normal form

JEL Classification: C72