# Spatial interactions and oscillatory tragedies of the commons

## TL;DR

This paper explores how spatial interactions and feedback mechanisms can cause oscillatory tragedies of the commons, revealing new emergent dynamics and potential ways to prevent resource depletion.

## Contribution

It introduces a novel framework combining stochastic and mean field models to analyze long-term feedback and spatial effects in tragedies of the commons.

## Key findings

- Oscillatory TOC-s emerge from payoff-dependent transition rules.
- Spatial interactions lead to cooperative wave fronts and cluster formation.
- Emergent dynamics suggest new mechanisms for TOC prevention.

## Abstract

A tragedy of the commons (TOC) occurs when individuals acting in their own self-interest deplete commonly-held resources, leading to a worse outcome than had they cooperated. Over time, the depletion of resources can change incentives for subsequent actions. Here, we investigate long-term feedback between game and environment across a continuum of incentives in an individual-based framework. We identify payoff-dependent transition rules that lead to oscillatory TOC-s in stochastic simulations and the mean field limit. Further extending the stochastic model, we find that spatially explicit interactions can lead to emergent, localized dynamics, including the propagation of cooperative wave fronts and cluster formation of both social context and resources. These dynamics suggest new mechanisms underlying how TOCs arise and how they might be averted.