Stochastic Stability of a Recency Weighted Sampling Dynamic

TL;DR

This paper models how long-term social conventions form through recency-weighted sampling of past interactions, showing convergence to stable mixed equilibria within certain minimal configurations.

Contribution

It introduces a novel Markov model for long-run convention formation based on recency-weighted sampling and analyzes its asymptotic behavior within minimal CURB blocks.

Findings

Unique asymptotic distribution concentrates on minimal CURB blocks.

Conditions established for convergence to mixed equilibrium conventions.

Methodology applicable to broader classes of learning models.

Abstract

We introduce and study a model of long-run convention formation for rare interactions. Players in this model form beliefs by observing a recency-weighted sample of past interactions, to which they noisily best respond. We propose a continuous state Markov model, well-suited for our setting, and develop a methodology that is relevant for a larger class of similar learning models. We show that the model admits a unique asymptotic distribution which concentrates its mass on some minimal CURB block configuration. In contrast to existing literature of long-run convention formation, we focus on behavior inside minimal CURB blocks and provide conditions for convergence to (approximate) mixed equilibria conventions inside minimal CURB blocks.