The noisy veto-voter model: a Recursive Distributional Equation on [0,1]

TL;DR

This paper investigates a recursive distributional equation on [0,1], identifying all invariant distributions, their basins of attraction, and analyzing endogeny in the associated tree-structured problem.

Contribution

It provides a complete characterization of invariant distributions and their basins for a specific RDE, extending recent results on endogeny.

Findings

All invariant distributions on [0,1] are identified.

The basins of attraction for these distributions are characterized.

The study extends Warren's results to address endogeny in this context.

Abstract

We study a particular example of a recursive distributional equation (RDE) on the unit interval. We identify all invariant distributions, the corresponding "basins of attraction" and address the issue of endogeny for the associated tree-indexed problem, making use of an extension of a recent result of Warren.