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# Timo Hiller

###### Friends and Enemies: A Model of Signed Network Formation, Theoretical Economics, 12, 2017, 1057-1087.

Supplementary Material

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, I 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.

Peer Effects in Endogenous Networks, Games and Economic Behavior, 105, 2017, 349-367.

Last Working Paper Version

This paper presents a model of strategic network formation with local complementarities in effort levels and positive local externalities. Results are obtained for a general class of payoff functions, which subsumes the linear-quadratic specification frequently used in theoretical and applied work. We assume homogeneous agents and characterize equilibria for two-sided and one-sided link formation. (Pairwise) Nash equilibrium networks are nested split graphs, which are a strict subset of core-periphery networks. We highlight the relevance of the convexity of the value function for obtaining these structures. More central agents are shown to exert more effort and obtain higher gross payoffs in equilibrium. However, net of linking cost, central agents may obtain strictly lower net payoffs. The curvature of the value function is also important for efficiency considerations. These findings are relevant for many social and economic phenomena, such as educational attainment, criminal activity, labor market participation, and R&D expenditures of firms. relations, and applied physics.

A simple model of network formation with competition effects, Journal of Mathematical Economics, Vol. 22, 2022.

This paper provides a game-theoretic model of network formation with a continuous effort choice. Efforts are strategic complements for direct neighbors in the network and display global substitution/competition effects. We show that if the parameter governing local strategic complements is larger than the one governing global strategic substitutes, then all pairwise Nash equilibrium networks are nested split graphs. We also consider the problem of a planner, who can choose effort levels and place links according to a network cost function. Again all socially optimal configurations are such that the network is a nested split graph. However, the socially optimal network may be different from equilibrium networks and efficient effort levels do not coincide with Nash equilibrium effort levels. In the presence of strategic substitutes, Nash equilibrium effort levels may be too high or too low relative to efficient effort levels. The relevant applications are crime networks and R&D collaborations among firms, but also interbank lending and trade.

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