An Equilibrium Analysis of Scrip Systems

TL;DR

This paper models scrip systems using game theory, showing that agents' wealth distribution can be characterized by relative entropy when they follow threshold strategies, and provides an algorithm to compute equilibrium states.

Contribution

It introduces a game-theoretic framework for scrip systems, demonstrating the existence of pure strategy equilibria with threshold strategies and offering a method to compute these equilibria.

Findings

We can characterize wealth distribution using relative entropy.

Scrip systems have pure strategy equilibria with threshold strategies.

An algorithm to compute equilibrium distributions is provided.

Abstract

A game-theoretic model of scrip (artificial currency) systems is analyzed. It is shown that relative entropy can be used to characterize the distribution of agent wealth when all agents use threshold strategies---that is, they volunteer to do work iff they have below a threshold amount of money. Monotonicity of agents' best-reply functions is used to show that scrip systems have pure strategy equilibria where all agents use threshold strategies. An algorithm is given that can compute such an equilibrium and the resulting distribution of wealth.