Why learning doesn’t add up: equilibrium selection with a composition of learning rules

In this paper, we investigate the aggregate behavior of populations of learning agents. We compare the outcomes in homogenous populations learning in accordance with imitate the best dynamics and with replicator dynamics to outcomes in populations that mix these two learning rules. New outcomes can emerge. In certain games, a linear combination of the two rules almost always attains an equilibrium that homogenous learners almost never locate. Moreover, even when almost all weight is placed on one learning rule, the outcome can differ from homogenous use of that rule. Thus, allowing even an arbitrarily small chance of using an alternative learning style can shift a population to select a different equilibrium.