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Cooperation in Evolving Social Networks

Doctoral Program in International Political Economy, Graduate School of Humanity and Social Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
Department of Economics, Columbia University, 1022 International Affairs Building, 420 West 118th Street, New York, New York 10027
Department of Mathematics and Statistics, 203 Lord House, University of Vermont, 16 Colchester Avenue, Burlington, Vermont 05401
Institute for Social and Economic Research and Policy, Columbia University, 8th Floor, International Affairs Building, 420 West 118th Street, New York, New York 10027 and Department of Sociology, Columbia University, 413 Fayerweather Hall, 1180 Amsterdam Avenue, New York, New York 10027
hanaki{at}dpipe.tsukuba.ac.jp
ap11{at}columbia.edu
pdodds{at}uvm.edu
djw24{at}columbia.edu

We study the problem of cooperative behavior emerging in an environment where individual behaviors and interaction structures coevolve. Players not only learn which strategy to adopt by imitating the strategy of the best-performing player they observe, but also choose with whom they should interact by selectively creating and/or severing ties with other players based on a myopic cost-benefit comparison. We find that scalable cooperation—that is, high levels of cooperation in large populations—can be achieved in sparse networks, assuming that individuals are able to sever ties unilaterally and that new ties can only be created with the mutual consent of both parties. Detailed examination shows that there is an important trade-off between local reinforcement and global expansion in achieving cooperation in dynamic networks. As a result, networks in which ties are costly and local structure is largely absent tend to generate higher levels of cooperation than those in which ties are made easily and friends of friends interact with high probability, where the latter result contrasts strongly with the usual intuition.

Key Words: networks-graphs; theory; games-group decisions; simulation
History: Received: May 11, 2005;