Regensburg 2004 – scientific programme

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DY: Dynamik und Statistische Physik

DY 34: Nonlinear Dynamics and Chaos I

DY 34.3: Talk

Wednesday, March 10, 2004, 15:00–15:15, H2

Minimal model for tag-based cooperation — •Arne Traulsen and Heinz Georg Schuster — Institut für theoretische Physik und Astrophysik, Christian-Albrechts Universität, Olshausenstr. 40, 24098 Kiel

Recently, Riolo et al. [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. We clarify the situation by solving a minimal mean-field version of the model of Riolo et al. [Traulsen and Schuster, Phys. Rev. E. 68, 046129 (2003)]. 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.