Abstract
We investigate whether replicator dynamics justify “survival of the fittest” when players inherit pure strategies, mixed strategies, or rules for choosing strategies. A strategy that never is a best reply can survive replicator dynamics if only pure strategies are heritable, but only rationalizable strategies survive if mixed strategies are heritable. Now suppose agents can inherit the rule of choosing a best reply to the last period's population, rather than inheriting a strategy itself. Such optimizers need not drive out players who inherit a dominated strategy. If we interpret replicator dynamics as a learning process, this means that non-optimizing behavior can survive.
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