Red Queen vs. Red King: When the Slowest Runner Wins the Race

Abstract

Many multi-population evolutionary games obtain multiple asymptotically stable equilibria. Unlike in the single population case, the size and location of the basins of attraction are determined partially by the relative speed of adjustment of the populations. This paper investigates the effect of differing adjustment speeds across populations on the relative strength of these equilibria under the two population standard replicator dynamics. The first step is to construct some simple measures of strength of equilibrium under the replicator dynamics. Together with a method for calculating boundaries of attraction basins in the two population case, this allows speed affects on equilibrium strength to be characterised in some simple 2 × 2 games. The results demonstrate the possibility of a “Red King” effect, whereby (relative) slow learning can be an advantage in simple strategic environments.