Cycles of Learning in the Centipede Game

This paper studies the evolutionary properties of the Centipede Game. For this game, the use of backward induction as a model of rational behavior has been consistently challenged by the experimental evidence. Our claim is that backward induction can still accurately predict the players’ behavior, provided that they are given time enough to appreciate the strategic environment in which they operate. We support this claim by proving convergence to the backward induction solution for all continuous-time monotonic selection dynamics. However, we also show that this solution is intrinsically unstable, and how this instability is positively related to the length of the game.