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.

The science of social networks is a central field of sociological study, a major application of random graph theory, and an emerging area of study by economists, statistical physicists and computer scientists. While these literatures are (slowly) becoming aware of each other, and on occasion drawing from one another, they are still largely distinct in their methods, interests, and goals. Here, my aim is to provide some perspective on the research from these literatures, with a focus on the formal modeling of social networks and the two major types of models: those based on random graphs and those based on game theoretic reasoning. I highlight some of the strengths, weaknesses, and potential synergies between these two network modeling approaches.

We examine the formation of networks among a set of players whose payo#s depend on the structure of the network. We focus on games where players may bargain by promising or demanding transfer payments when forming links. We examine several variations of the transfer/bargaining aspect of link formation. One aspect is whether players can only make and receive transfers to other players to whom they are directly linked, or whether they can also subsidize links that they are not directly involved in. Another aspect is whether or not transfers related to a given link can be made contingent on the full resulting network or only on the link itself. A final aspect is whether or not players can pay other players to refrain from forming links. We characterize the networks that are supported under these variations and show how each of the above aspects is related either to accounting for a specific type of externality, or to dealing with the combinatorial nature of network payo#s.

Previous allocation rules for network games, such as the Myerson Value, implicitly or explicitly take the network structure as fixed. In many situations, however, the network structure can be altered by players. This means that the value of alternative network structures (not just sub-networks) can and should influence the allocation of value among players on any given network structure. I present a family of allocation rules that incorporate information about alternative network structures when allocating value.

Recent analyses of social networks, both empirical and theoretical, are discussed, with a focus on how social networks influence economic behavior, as well as how social networks form. Some challenges of such research are discussed as are some of the important considerations for the literature going forward.

We model situations in which a principal provides incentives to a group of agents to participate in a project (such as a social event or a commercial activity). Agents’ benefits from participation depend on the identity of other participating agents. We assume bilateral externalities and characterize the optimal incentive mechanism. Using a graph-theoretic approach we show that the optimal mechanism provides a ranking of incentives for the agents, which can be described as arising from a virtual popularity tournament among the agents (similar to ones carried out by sport associations). Rather then simply ranking agents according to their measure of popularity, the optimal mechanism makes use of more refined two-way comparison between the agents. An implication of our analysis is that higher levels of asymmetry of externalities between the agents enable a reduction of the principal’s payment. In addition, contrary to intuition, an increase in the aggregate externalities, does not necessarily decrease principal’s payment, nor does it change agents rewards.

In this paper, we consider two classes of economic environments. In the first type, agents are faced with the task of providing local public goods that will benefit some or all of them. In the second type, economic activity takes place via formation of links. Agents need to both form a network and to decide how to share the output generated. For both scenarios, we suggest a bidding mechanism whereby agents bid for the right to decide upon the organization of economic activity. The subgame perfect equilibria of this game generate efficient outcomes. Acknowledgements: Pérez-Castrillo acknowledges financial support from BEC2000-