  We consider a model of learning and evolution in games whose action sets are
endowed with a partition-based similarity structure intended to capture
exogenous similarities between strategies. In this model, revising agents have
a higher probability of comparing their current strategy with other strategies
that they deem similar, and they switch to the observed strategy with
probability proportional to its payoff excess. Because of this implicit bias
toward similar strategies, the resulting dynamics - which we call the nested
replicator dynamics - do not satisfy any of the standard monotonicity
postulates for imitative game dynamics; nonetheless, we show that they retain
the main long-run rationality properties of the replicator dynamics, albeit at
quantitatively different rates. We also show that the induced dynamics can be
viewed as a stimulus-response model in the spirit of Erev & Roth (1998), with
choice probabilities given by the nested logit choice rule of Ben-Akiva (1973)
and McFadden (1978). This result generalizes an existing relation between the
replicator dynamics and the exponential weights algorithm in online learning,
and provides an additional layer of interpretation to our analysis and results.
