Mixed Populations of Conformists, Nonconformists, and Imitators

In two-strategy decision-making problems, individuals typically imitate the highest earners, choose the common strategy (conformists), or select the rare one (nonconformists). Populations consisting of imitators, conformists, and nonconformists can undergo perpetual fluctuations in strategy proportions. How these fluctuations evolve as population size increases was previously an open question. We show that the family of Markov chains describing discrete population dynamics forms a generalized stochastic approximation process for a differential inclusion—the continuous-time dynamics. By leverging results in stochastic approximation theory, we show that the amplitudes of fluctuations in the proportions of the two strategies approach zero with probability one when the population size grows. Our results suggest that large-scale perpetual fluctuations are unlikely in large, well-mixed populations, particularly when imitators follow the highest earners.

Mixed Populations of Conformists, Nonconformists, and Imitators

Monday, July 14 from 6:00pm - 9:00pm in

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Azadeh Aghaeeyan

"Mixed Populations of Conformists, Nonconformists, and Imitators"

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