Does good memory help you win games?

TL;DR

This paper investigates how varying memory lengths among agents influence competition in a resource-based game, revealing a critical memory threshold and a dynamical equilibrium through simulation and analytical methods.

Contribution

It introduces a simple game model linking memory length to resource competition, with analytical insights connecting memory to temperature in urn models.

Findings

Existence of a critical memory length causing instability.

Different memory lengths can coexist in equilibrium.

Analytical connection between memory and temperature in urn models.

Abstract

We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths can compete and co-exist in a dynamical equilibrium. Our analytical formulation makes a connection to statistical urn models, and we show that temperature is mirrored by the agent's memory. Our analysis is easily generalisable to many other game models with implications that we briefly discuss.