Friends and enemies: a model of signed network formation

Timo C Hiller

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)
574 Downloads (Pure)


I propose a simple model of signed network formation, where agents make friends to extract payoffs from weaker enemies. The model thereby accounts for the interplay between friendship and alliance on one hand and enmity and antagonism on the other. Nash equilibrium configurations are such that, either everyone is friends with everyone, or agents can be partitioned into different sets, where agents within the same set are friends and agents in different sets are enemies. Any strong Nash equilibrium must be such that a single agent is in an antagonistic relationship with everyone else. Furthermore, we show that Nash equilibria cannot be Pareto ranked. This paper offers a game-theoretic foundation for a large body of work on signed networks, called structural balance theory, which has been studied in sociology, social psychology, bullying, international relations and applied physics. The paper also contributes to the literature on contests and economics of conflict.
Original languageEnglish
Pages (from-to)1057–1087
Number of pages31
JournalTheoretical Economics
Early online date22 Sep 2017
Publication statusPublished - Sep 2017

Structured keywords

  • ECON Microeconomic Theory


  • Signed network formation
  • structural balance
  • contest success function
  • bullying
  • economics of conflict
  • international relations


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