Self-Organization and Emergence in Social Systems: Modeling the Coevolution of Social Environments and Cooperative Behavior

Abstract

We demonstrate with computational simulation scenarios how social environments and individual behavior coevolve and how fundamentally different macro-effects emerge, when separate micromechanisms are combined. Our framework considers social interactions among agents on a spatial grid or in networks. In the Prisoner's Dilemma, neither imitation of more successful strategies nor the migration to more favorable locations can promote cooperation. However, when both microscopic mechanisms are combined, they cause the segregation of cooperators and defectors, and the self-organization of cooperative clusters on the macro-level. These are robust to randomness, while cooperation may break down in a “globalized society.” The implications for the evolution of norms and institutions are discussed.

Keywords:

• agent-based simulation
• cooperation
• migration
• mobility
• representative agent models
• self-organization and emergence
• social dilemmas
• social learning and imitation
• social networks
• spatial games

Acknowledgments

We would like to thank Karl-Dieter Opp, three anonymous reviewers, and the three editors of this special issue for their insightful, constructive and extensive comments.

Notes

¹See the simulation movies at http://www.univie.ac.at/virtuallabs/Snowdrift/struct.pure.html and compare them with the ones for migration games at http://www.soms.ethz.ch/migrationgames

²Note that this treatment can be replaced by one, where the payoff is updated whenever one is a focal individual or an interaction partner. This does not change our main conclusions.

³Note that our main conclusions also apply, if the the order of update steps is inter-changed, see Yu and Helbing (2010) and http://www.soms.ethz.ch/migrationgames.

⁴Videos of related simulations are available at http://www.soms.ethz.ch/migrationgames.

⁵This generally applies, when the payoff differences T − R and P − S are not too big; see Figure 2 in (Helbing and Yu, 2008) and Figure 6 in (Helbing and Yu, 2009) for related results. If the imitation rule would be replaced by a myopic (one-stage) best response rule, individuals in a cooperative cluster may trust on the cooperation in the neighborhood in the next time step and decide to defect. However, if everybody would behave this way, the resulting payoff would be just mS rather than mT, i.e., quite poor. Therefore, an argument along the line of group selection would suggest that communities with a best response behavior (pursuing a short-sighted profit maximization) should die out in the course of time when competing with communities following an imitation behavior as assumed in our model.

⁶For example, imagine a job offer by an internationally oriented university or a love affair during the holidays.

⁷Note that changing the order of the update steps does not question our main conclusions. Nevertheless, it changes the appearance of the resulting spatio-temporal patterns and the sensitivity to noise. For a discussion see Yu and Helbing (2010) and http://www.soms.ethz.ch/migrationgames.

⁸As we show in Section 2.2, the initial condition does not matter for the final level of cooperation, when noise is taken into account. Starting with a circular configuration, however, makes the effects of the different kinds of noise better visible.

⁹For a study of density-dependent effects in a similar model without noise, see Helbing and Yu (2008).

¹⁰Note however, that it matters a lot how quickly cooperators can build up cooperative clusters as compared to the rate at which they are destroyed by defector invasion and by noise effects.

¹¹We analyzed simulation scenarios for other kinds of networks, for example, scale free networks, as well. Our preliminary results lead to similar conclusions.

¹²This can be best seen in visualizations of simulation runs provided at http://www.soms.ethz.ch/migrationgames.

¹³In linear models, all system properties can be derived by adding up the properties of its elements.

¹⁴Similar results are found, when global interacions with everybody are replaced by interactions with m = 4 randomly chosen interaction partners anywhere in the grid, creating “well-mixed” interactions.

¹⁵For related discussions on punishment and surveillance institutions along with experimental data, see Gürerk, Irlenbusch, and Rockenbach (2006), Rauhut (2009), Rauhut and Junker (2009), Groeber and Rauhuf (2010).