The multilayer garbage disposal game

TL;DR

This paper introduces a mathematical analysis of the multilayer garbage disposal game, showing that under certain conditions, all agents' garbage levels converge to the initial average, highlighting the role of initial conditions in outcomes.

Contribution

The paper provides a novel mathematical perspective on the multilayer garbage disposal game, analyzing convergence properties without relying on traditional game theory.

Findings

All agents' garbage converges to the initial average when social graphs are connected.

Winners are agents with initial total garbage above the overall average.

Convergence occurs across all layers under specified conditions.

Abstract

The multilayer garbage disposal game is an evolution of the garbage disposal game. Each layer represents a social relationship within a system of finitely many individuals and finitely many layers. An agent can redistribute their garbage and offload it onto their social neighbors in each layer at each time step. We study the game from a mathematical perspective rather than applying game theory. We investigate the scenario where all agents choose to average their garbage before offloading an equal proportion of it onto their social neighbors. It turns out that the garbage amounts of all agents in all layers converge to the initial average of all agents across all layers when all social graphs are connected and have order at least three. This implies that the winners are those agents whose initial total garbage exceeds the average total garbage across all agents.