Strategy-specific barriers to learning and nonmonotonic selection dynamics

The replicator dynamics are generalized to allow for strategy-specific barriers to learning. The resulting dynamics satisfy neither payoff monotonicity nor payoff positivity, but do satisfy weak payoff positivity. It is shown that initial states from which trajectories converge to a rest point under the replicator dynamics may yield trajectories which approach a stable limit cycle under the generalized replicator dynamics. Furthermore, strategies which are strictly dominated by other pure strategies may survive indefinitely along such nonconvergent paths. (C) 1998 Academic Press.