A Minimal Model for Tag-based Cooperation

TL;DR

This paper presents a minimal model explaining how fluctuations in tolerance levels among agents can lead to sustained cooperation and biodiversity, highlighting the role of stochastic transitions and bifurcations.

Contribution

The authors introduce a simplified model that identifies stochastic tolerance shifts and bifurcations as key to understanding cooperation dynamics and biodiversity.

Findings

Oscillations of tolerance support arise from random transitions.

Biodiversity is maintained through these tolerance fluctuations.

Oscillation frequency scales linearly with transition rate.

Abstract

Recently, Riolo et al. [R. L. Riolo et al., Nature 414, 441 (2001)] showed by computer simulations that cooperation can arise without reciprocity when agents donate only to partners who are sufficiently similar to themselves. One striking outcome of their simulations was the observation that the number of tolerant agents that support a wide range of players was not constant in time, but showed characteristic fluctuations. The cause and robustness of these tides of tolerance remained to be explored. Here we clarify the situation by solving a minimal version of the model of Riolo et al. It allows us to identify a net surplus of random changes from intolerant to tolerant agents as a necessary mechanism that produces these oscillations of tolerance which segregate different agents in time. This provides a new mechanism for maintaining different agents, i.e. for creating biodiversity. In our model the transition to the oscillating state is caused by a saddle node bifurcation. The frequency of the oscillations increases linearly with the transition rate from tolerant to intolerant agents.