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Free keywords:
game theory; microscopic assumptions; stochastic dynamics
Abstract:
Themodeling of evolutionary game dynamics in finite populations requiresmicroscopic processes
that determine howstrategies spread. The exact details of these processes are often chosenwithout
much further consideration.Different types ofmicroscopicmodels, including in particular fitnessbased
selection rules and pairwise comparison dynamics, are often used as if theywere interchangeable.
We challenge this viewand investigate howrobust these choices on themicro-level really are.We
focus on a keymacroscopic quantity, the probability for a singlemutant to take over a population of
wild-type individuals.We showthat even in unstructured populations there is only one pair of a fitness-
based process and a pairwise comparison process leading to identical outcomes for arbitrary
games and for all intensities of selection. This strong restriction is not relaxed evenwhen the class of
pairwise comparison processes is broadened. This highlights the perils ofmaking arbitrary choices at
themicro-levelwithout regard of the consequences at themacro-level.
