Best-reply matching and the centipede game.

In their paper on Best-Reply Matching (BRM), Droste, Kosfeld & Voorneveld (2003) obtained quite intuitive results for the centipede game. In this short paper we first show that these results derive from the application of their criterion to the reduced normal form of the game. Then we prove that applying their criterion to the normal form of the game leads to different results. Third we propose an extension of Droste, Kosfeld & Voorneveld’s criterion, which leads to the same results in both the reduced normal form and the normal form of a game. This extension leads to a larger set of behaviors, including the Subgame Perfect Nash equilibrium but also a limited rationality behavior that strongly sustains the continuation of the game.