Learning, Matching and Aggregation

Fictitious play and ``gradient'' learning are examined in the context of a large population where agents are repeatedly randomly matched. We show that the aggregation of this learning behaviour can be qualitatively different from learning at the level of the individual. This aggregate dynamic belongs to the same class of simply defined dynamic as do several formulations of evolutionary dynamics. We obtain sufficient conditions for convergence and divergence which are valid for the whole class of dynamics. These results are therefore robust to most specifications of adaptive behaviour.