Friends and enemies: A model of signed network formation

I propose a game of signed network formation, where agents make friends to coerce payoffs from enemies with fewer friends. The model accounts for the interplay between friendship and enmity. Nash equilibrium configurations are such that, either everyone is friends with everyone, or agents can be partitioned into sets of different size, where agents within the same set are friends and agents in different sets are enemies. These results mirror findings of a large body of work on signed networks in sociology, social psychology, international relations and applied physics. ∗Department of Economics, University of Bristol, 8 Woodland Road, Bristol BS8 1TN, UK (email: [email protected]). This paper is based on the second chapter of my Ph.D. dissertation at the European University Institute. A previous version was titled “Alliance Formation and Coercion in Networks.” I am grateful to my advisors Fernando Vega-Redondo and Massimo Morelli for their invaluable support and guidance. I also thank Dilip Abreu, Sergio Currarini, Matthew O. Jackson, David K. Levine, In-Uck Park, Paolo Pin, Brian Roberson, Tomas Sjöström, Francesco Squintani, participants of the Networks Working Group at the European University Institute, seminar participants at the Institute for Advanced Studies (Princeton), FGV-Rio, CORE (Université catholique de Louvain), University of Vienna, Ludwig Maximilian University of Munich, Universitat de Barcelona, University of Bristol, PUC-Rio and participants of SAET 2011, CTN 2011 and the UECE Lisbon Meetings 2010 for helpful comments. All remaining errors are mine.