Stochastic Redistribution of Indistinguishable Items in Shared Habitation: A Multi-Agent Simulation Framework

TL;DR

This paper introduces a stochastic multi-agent simulation model to analyze how indistinguishable items like socks are redistributed among cohabitants, revealing emergent asymmetries and disorder in shared domestic systems.

Contribution

It presents a novel discrete-event stochastic framework combining ecological and diffusion concepts to model item redistribution among agents.

Findings

Minimal exchange probabilities lead to asymmetries.

Emergent quasi-equilibrium distributions observed.

Stochastic processes cause persistent imbalances.

Abstract

This paper presents a discrete-event stochastic model for the redistribution of indistinguishable personal items, exemplified by socks, among multiple cohabitants sharing a communal laundry system. Drawing on concepts from ecological population dynamics, diffusion processes, and stochastic exchange theory, the model captures the probabilistic mechanisms underlying item mixing, recovery, and loss. Each cohabitant is represented as an autonomous agent whose belongings interact through iterative cycles of collective washing, sorting, and partial correction. The system's evolution is characterized by random mixing events, selective recollection, and attrition over time. Implemented using the SimPy discrete-event simulation framework, the model demonstrates that even minimal exchange probabilities can generate emergent asymmetries, quasi-equilibrium distributions, and long-term disorder. The findings illustrate how stochastic processes inherent to shared domestic systems can produce persistent imbalances, offering a quantitative perspective on an everyday social phenomenon.