Cooperation in Anonymous Dynamic Social Networks ∗ Preliminary Working

We study the extent to which cooperative behavior can be sustained in large, anonymous, evolving social networks. Individuals strategically form relationships under a social matching protocol and engage in prisoner’s dilemma interactions with their partners. We characterize a class of equilibria that support cooperation as a stationary outcome. When cooperation is possible, its level is uniquely determined. While neither community enforcement nor contagion mechanisms have force in our setting, the endogenous dynamics of the social network imply that cooperation allows an individual to gradually accumulate a large network of profitable interactions, while defection results in social marginalization. Even as players become perfectly patient, equilibrium allows for full cooperation, only autarky, or the coexistence of cooperation and defection, depending on payoffs. Smaller levels of cooperation can be sustained by a form of exclusivity among cooperators. ∗We thank Simon Board, Wiola Dziuda, Matthew Jackson, Christoph Kuzmics, David Miller, Paolo Pin, Marzena Rostek, Bill Sandholm, Joel Sobel, Joel Watson and Simon Weidenholzer for helpful comments and conversations. †University of Toronto, Toronto, ON Canada, [email protected] ‡MEDS, Kellogg and NICO, Northwestern University, Evanston, IL USA, [email protected] §Northwestern University, Evanston, IL USA. [email protected]