Essays on social and economic networks

Abstract

This thesis consists of three papers in the field of social and economic networks. In the first, called "Peer Effects in Endogenous Networks", I build a model of endogenous net- work formation in the presence of peer effects, which play an important role for decisions concerning educational attainment, criminal activity, labor market participation and R&D expenditures of firms. The class of payoff functions assumed induce local complementarities in effort levels and positive local externalities. Links are one-sided and agents move simultaneously in links and effort levels. I find that equilibrium networks display - other than the complete and the empty network - a core-periphery structure, which is commonly observed in empirical studies. Ex-ante homogenous agents may obtain very different ex-post outcomes, depending on the network that arises in equilibrium. Multiplicity of equilibria serves as an explanation for large differences in behaviour across otherwise identical groups. The second paper, titled "Alliance Formation and Coercion in Networks", presents a game-theoretic model of network formation, which allows agents to enter bilateral alliances and to extract payoffs from enemies. Each pair of agents creates a surplus of one, which allies divide in equal parts. If agents are enemies, then the agent with more allies obtains a larger share of the surplus. I show that Nash equilibria are of two types. First, a state of utopia, where all agents are allies. Second, asymmetric equilibria, such that agents can be partitioned into sets of different size, where agents within the same set are allies and agents in different sets are enemies. These results stand in contrast to coalition formation games in the economics of conflict literature, where stable group structures are generally symmetric. The model also provides a game-theoretic foundation for structural balance, a long-standing notion in social psychology, which has been fruitfully applied to the study of alliance formation in international relations. The third paper, "A Note on Stochastically Stable States for ‘Alliance Formation and Coercion in Networks’", introduces dynamics into the model of the second paper and provides a conjecture for stochastically stable states. At every time period t and with fixed probability p, each agent adjusts his strategy myopically, while with small probability E he chooses his strategy at random. The configuration where all agents sustain only positive links is shown to not be stochastically stable. Stochastically stable state are thought to be such that the number of cliques is maximal, under a restriction on the relative size of groups.