Dynamic Models of Appraisal Networks Explaining Collective Learning

This paper proposes models of learning process in teams of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model, and discuss conditions of suboptimality. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science.

💡 Research Summary

The paper develops a series of mathematically rigorous models that describe how a team of individuals collectively learns the relative skill levels of its members while repeatedly executing tasks. The authors start with a simple centralized manager model and progressively introduce more realistic social mechanisms, culminating in a fully integrated model that couples interpersonal appraisal, influence, and task assignment dynamics.

Manager dynamics (centralized)
A team of n agents has fixed but unknown skill vector x. Each task has unit total workload that can be split among agents according to a probability vector w (the assignment). Individual performance is modeled as p_i(w)=f(x_i / w_i) where f is increasing, concave, and continuously differentiable (e.g., a power law with exponent 0<γ<1). An external manager observes the performance vector p(w) and updates the assignment using a continuous‑time replicator equation:

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