Garbage disposal game on finite graphs

TL;DR

This paper studies a garbage disposal game on finite graphs where individuals exchange garbage with neighbors under certain conditions, showing convergence to average garbage levels in specific network structures.

Contribution

It introduces a threshold-based rule for garbage exchange and proves convergence properties on connected social graphs excluding star graphs.

Findings

Garbage levels converge to the initial average on connected non-star graphs.

Without the threshold, the process always converges to the average.

The model extends understanding of local exchange dynamics in social networks.

Abstract

The garbage disposal game involves a finite set of individuals, each of whom updates their garbage by either receiving from or dumping onto others. We examine the case where only social neighbors, whose garbage levels differ by a given threshold, can offload an equal proportion of their garbage onto others. Remarkably, in the absence of this threshold, the garbage amounts of all individuals converge to the initial average on any connected social graph that is not a star.