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This paper studies the effect of randomness in per-period matching
on the long-run outcome of non-equilibrium adaptive processes.
If there are many matchings between each strategy revision, the randomness
due to matching will be small; our question is when a very
small noise due to matching has a negligible effect. We study two
different senses of this idea, and provide sufficient conditions for each.
The less demanding sense corresponds to sending the matching noise
to zero while holding fixed all other aspects of the adaptive process.
The second sense in which matching noise can be negligible is that
it doesn’t alter the
limit distribution obtained as the limit of the invariantdistributions as an exogeneous “mutation rate” goes to zero.
When applied to a model with mutations, the difference between these
two senses is in the order of limits: the first sense asks for continuity
of e.g. the ergodic distribution in the matching noise holding the mutation
rate fixed, whereas the second sense asks for continuity of the
limit distribution in the matching noise.
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