Stochastic analysis of an agent-based model

TL;DR

This paper provides an analytical stochastic framework for an agent-based forecasting game, revealing how information cascades and herd behavior emerge, with precise results in herd-dominant scenarios.

Contribution

It introduces a Langevin equation approach to model the dynamics of agents in a forecasting game with herd behavior and analyzes collective phenomena via Kramers' problem.

Findings

Accurately describes herd dynamics using Langevin equations

Identifies conditions leading to information cascades

Provides analytical solutions matching simulations in herd regimes

Abstract

We analyze the dynamics of a forecasting game which exhibits the phenomenon of information cascades. Each agent aims at correctly predicting a binary variable and he/she can either look for independent information or herd on the choice of others. We show that dynamics can be analitically described in terms of a Langevin equation and its collective behavior is described by the solution of a Kramers' problem. This provides very accurate results in the region where the vast majority of agents herd, which corresponds to the most interesting one from a game theoretic point of view.