The Dynamics of Coalition Formation on Complex Networks

S. Auer*, J. Heitzig, U. Kornek, E. Schoell, J. Kurths

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)
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Complex networks describe the structure of many socio-economic systems. However, in studies of decision-making processes the evolution of the underlying social relations are disregarded. In this report, we aim to understand the formation of self-organizing domains of cooperation ("coalitions") on an acquaintance network. We include both the network's influence on the formation of coalitions and vice versa how the network adapts to the current coalition structure, thus forming a social feedback loop. We increase complexity from simple opinion adaptation processes studied in earlier research to more complex decision-making determined by costs and benefits, and from bilateral to multilateral cooperation. We show how phase transitions emerge from such coevolutionary dynamics, which can be interpreted as processes of great transformations. If the network adaptation rate is high, the social dynamics prevent the formation of a grand coalition and therefore full cooperation. We find some empirical support for our main results: Our model develops a bimodal coalition size distribution over time similar to those found in social structures. Our detection and distinguishing of phase transitions may be exemplary for other models of socio-economic systems with low agent numbers and therefore strong finite-size effects.

Original languageEnglish
Article number13386
Number of pages8
JournalScientific Reports
Early online date25 Aug 2015
Publication statusPublished - 25 Aug 2015

Bibliographical note

This work was carried out within the framework of PIK’s COPAN project. We gratefully acknowledge funding by the German Federal Ministry of Education and Research (BMBF) via the CoNDyNet project, grant no. 03SF0472A, and of the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with Institute of Applied Physics RAS). We thank Jonathan Donges for helpful discussions on this manuscript.


  • size distribution
  • school size
  • evolution


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