I survey the recent literature on the formation of networks. I provide definitions of network games, a number of examples of models from the literature, and discuss some of what is known about the (in)compatibility of overall societal welfare with individual incentives to form and sever links.

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Abstract Using original data on gifts and loans, this paper investigates how rural Filipino households deal with income and expenditure shocks. Results indicate that gifts and informal loans are partly motivated by consumption smoothing motives but do not serve to efficiently share risk. Certain shocks are better insured through gifts and loans than others. Mutual insurance does not take place at the village level; rather, households receive help primarily through networks of friends and relatives. Network quality matters. Risk is shared through flexible, zero interest informal loans rather than gifts. The evidence is consistent with models of quasi-credit where enforcement constraints limit gift giving.

A strong equilibrium (Aumann 1959) is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy to be the ratio of the worst case strong equilibrium to the social optimum. In contrast to the traditional price of anarchy, which quantifies the loss incurred due to both selfishness and lack of coordination, the strong price of anarchy isolates the loss originated from selfishness from that obtained due to lack of coordination. We study the strong price of anarchy in two settings, one of job scheduling and the other of network creation. In the job scheduling game we show that for unrelated machines the strong price of anarchy can be bounded as a function of the number of machines and the size of the coalition. For the network creation game we show that the strong price of anarchy is at most 2. In both cases we show that a strong

This paper studies a model of dynamic network formation when individuals are farsighted: players evaluate the desirability of a “current ” move in terms of its consequences on the entire discounted stream of payoffs. We define a concept of equilibrium which takes into account far-sighted behavior of agents and allows for limited cooperation amongst agents. We show that an equilibrium process of network formation exists. We also show that there are network structures in which no equilibrium strategy profile can sustain efficient networks. We then provide sufficient conditions under which the equilibrium process will yield efficient outcomes.

This paper provides a survey of recent experimental work in economics focusing on social and economic networks. The experiments consider networks of coordination and cooperation, buyerseller networks, and network formation. 1

We consider a setting where every pair of players that undertake a transaction (e.g. exchange goods or information) create a unit surplus. A transaction can take place only if the players involved have a connection. If the connection is direct the two players split the surplus equally while if it is indirect then intermediate players also get an equal share of the surplus. Thus individuals form links with others to create surplus, to gain intermediation rents and to circumvent others who are trying to become intermediary. Our analysis clari…es the interplay between these forces in the process of strategic network formation. First, we show that, in the absence of capacity constraints on links, it leads to the emergence of a star network where a single agent acts as an intermediary for all transactions and enjoys signi…cantly higher payo¤s. Second, we study the implications of capacity constraints in the ability of agents to form links. In this case, distances between players must be long, which induces players who are “far o¤” to connect in order to avoid paying large intermediation rents. A cycle network then emerges, payo¤s being equal across all players.

This paper studies bilateral insurance schemes across networks of individuals. While transfers are based on social norms, each individual must have the incentive to abide by those norms, and so we investigate the structure of self-enforcing insurance networks. Network links play two distinct and possibly conflictual roles. First, they act as conduits for transfers. Second, they act as conduits for information. These features affect the scope for insurance, as well as the severity of punishments in the event of noncompliance. Their interaction leads to a characterization of stable networks as networks which are suitably “sparse”, the degree of sparseness being related to the length of the minimal cycle that connects any triple of agents. As corollaries, we find that both “thickly connected” networks (such as the complete graph) and “thinly connected” networks (such as trees) are likely to be stable, whereas intermediate degrees of connectedness jeopardize stability. Finally, we study in more detail the notion of networks as conduits for transfers, by simply assuming a punishment structure (such as autarky) that is independent of the precise architecture of the network. This allows us to isolate a bottleneck effect: the presence of certain key agents who act as bridges for several transfers. Bottlenecks are captured well in a feature of trees that we call decomposability, and we show that all decomposable networks have the same stability properties and that these are the least likely to be stable.

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The study of bargaining has a long history, but many basic settings are still rich with unresolved questions. In particular, consider a set of agents who engage in bargaining with one another, but instead of pairs of agents interacting in isolation, agents have the opportunity to choose whom they want to negotiate with, along the edges of a graph representing social-network relations. The area of network exchange theory in sociology has developed a large body of experimental evidence for the way in which people behave in such network-constrained bargaining situations, and it is a challenging problem to develop models that are both mathematically tractable and in general agreement with the results of these experiments. We analyze a natural theoretical model arising in network