Comparative Patience

TL;DR

This paper introduces a new way to compare patience levels of agents based on their preferences over prize sequences and characterizes this comparison through their discounting behaviors.

Contribution

It formulates a dominance criterion for prize sequences and fully characterizes the comparative patience relation in terms of agents' discount rules.

Findings

A dominance criterion for prize sequences is established.

A formal definition of comparative patience is provided.

The relation is characterized by agents' discount functions.

Abstract

We begin by formulating and characterizing a dominance criterion for prize sequences: $x$ dominates $y$ if any impatient agent prefers $x$ to $y$. With this in hand, we define a notion of comparative patience. Alice is more patient than Bob if Alice's normalized discounted utility gain by going from any $y$ to any dominating $x$ is less than Bob's discounted utility gain from such an improvement. We provide a full characterization of this relation in terms of the agents' discount rules.