Dynamic social learning under graph constraints

TL;DR

This paper introduces a model of social learning constrained by graph structures, linking it to reinforced random walks, and analyzes its asymptotic behavior as reinforcement intensifies.

Contribution

It establishes a novel connection between graph-constrained dynamic choice models and vertex reinforced random walks, providing insights into their long-term outcomes.

Findings

Asymptotic outcomes concentrate around the optimum as reinforcement increases.

The empirical process is equivalent to a vertex reinforced random walk.

The model extends understanding of social learning dynamics under constraints.

Abstract

We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively $\alpha$-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov noise, has the same probability law as a certain vertex reinforced random walk. We use this equivalence to show that for $\alpha > 0$, the asymptotic outcome concentrates around the optimum in a certain limiting sense when `annealed' by letting $\alpha\uparrow\infty$ slowly.