Does Noise Undermine the First-Mover Advantage? An Evolutionary Analysis of Bagwell's Example

Abstract

Bagwell (1995) considered a simple Stackelberg-type game in which one player benefits from the other's ability to observe his move, assuming they play the unique subgame perfect equilibrium. He showed that introducing noise in the observability of the move eliminates that equilibrium, and thus the advantage. Van Damme and Hurkens (1997) objected that the noisy game also has a mixed strategy equilibrium close to the pure strategy one Bagwell had eliminated. However, we analyse the noisy game with a wide variety of evolutionary and learning dynamics, and find that almost all admit the no-first-mover-advantage equilibrium as a possible outcome, and often they select it uniquely.