Minimal model for tag-based cooperation

Arne Traulsen and Heinz Georg Schuster
Phys. Rev. E 68, 046129 – Published 27 October 2003
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Abstract

Recently, Riolo et al. [Nature (London) 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.

  • Received 17 July 2003

DOI:https://doi.org/10.1103/PhysRevE.68.046129

©2003 American Physical Society

Authors & Affiliations

Arne Traulsen* and Heinz Georg Schuster

  • Institut für Theoretische Physik und Astrophysik, Christian-Albrechts Universität, Olshausenstraße 40, 24098 Kiel, Germany

  • *Electronic address: traulsen@theo-physik.uni-kiel.de

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Issue

Vol. 68, Iss. 4 — October 2003

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