A Survey of Models of Network Formation: Stability and Efficiency

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 Stability and Efficiency of Economic and Social Networks

This paper studies the formation of networks among individuals. The focus is on the compatibility of overall societal welfare with individual incentives to form and sever links. The paper reviews and synthesizes some previous results on the subject, and also provides new results on the existence of pairwise-stable networks and the relationship between pairwise stable and efficient networks in a variety of contexts and under several definitions of efficiency.networks, network formation, stability, efficiency, social networks

Allocation Rules for Network Games

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.networks, network games, allocation rules

Efficiency and Information Aggregation in Auctions with Costly Information

Consider an auction in which $k$ identical objects are sold to $n>k$ bidders who each have a value for one object which can have both private and common components to it. Private information concerning the common component of the object is not exogenously given, but rather endogenous and bidders face a cost to becoming informed. If the cost of information is not prohibitively high, then the equilibrium price in a uniform price auction will not aggregate private information, in contrast to the costless information case. Moreover, for a wide class of auctions if the cost of information is not prohibitively high then the objects can only be allocated in a weakly efficient sense, and then only if the equilibrium proportion of endogenously informed agents is vanishing as the economy grows. In spite of these results, it is shown that there is a mechanism for which there exist equilibria and for which (weak) efficiency is achieved as the economy grows in the face of endogenous information acquisition.Auctions, Efficiency, Information Acquisition, Information Aggregation

Allocation Rules for Network Games

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.Networks, Network Games, Allocation Rules, Cooperative Games

Diffusion of Behavior and Equilibrium Properties in Network Games

Situations in which agents’ choices depend on choices of those in close proximity, be it social or geographic, are ubiquitous. Selecting a new computer platform, signing a political petition, or even catching the flu are examples in which social interactions have a significant role. While some behaviors or states propagate and explode within the population (e.g., Windows OS, the HIV virus) others do not (e.g., certain computer viruses). Our goal in this paper is twofold. First, we provide a general dynamic model in which agents’ choices depend on the underlying social network of connections. Second, we show the usefulness of the model in determining when a given behavior expands within a population or disappears as a function of the environment’s fundamentals. We study a framework in which agents face a choice between two actions, 0 and 1 (e.g., whether to pursue a certain level of education, switch to Linux OS, etc.). Agents are linked through a social network, and an agent’s payoffs from each action depend on the number of neighbors she has and her neighbors’ choices. The diffusion process is defined so that at each period, each agent best responds to the actions taken by her neighbors in the previous period, assuming that her neighbors follow the population distribution of actions (a mean-field approximation). Steady states correspond to equilibria of the static game. Under some simple conditions, equilibria take one of two forms. Some are stable, so that a slight perturbation to any such equilibrium would lead the diffusion process to converge back to that equilibrium point. Other equilibria are unstable, so that a slight change in the distribution of actions leads to a new distribution of actions and eventually to a stable steady state. We call such equilibria tipping points. We analyze how the environment’s fundamentals (cost distribution, payoffs, and network structure) affect the set of equilibria, and characterize the adoption patterns within the network. The paper relates to recent work on network games and network diffusion, including work by Stephen Morris (2000); Pastor-Satorras and Vespignani (2000); Mark E. J. Newman (2002); Dunia López-Pintado (2004); Jackson and Brian W. Rogers (2007); Jackson and Yariv (2005); and Andrea Galeotti et al. (2005, henceforth GGJVY). Its contribution is in characterizing diffusion of strategic behavior and analyzing the stability properties of equilibria, and employing methods that allow us to make comparisons across general network structures and settings. Given that social networks differ substantially and systematically in structure across settings (e.g., ethnic groups, professions, etc.), understanding the implications of social structure on diffusion is an important undertaking for a diverse set of applications

Diffusion in Networks and the Unexpected Virtue of Burstiness

Whether an idea, information, infection, or innovation diffuses throughout a society depends not only on the structure of the network of interactions, but also on the timing of those interactions. Recent studies have shown that diffusion can fail on a network in which people are only active in "bursts", active for a while and then silent for a while, but diffusion could succeed on the same network if people were active in a more random Poisson manner. Those studies generally consider models in which nodes are active according to the same random timing process and then ask which timing is optimal. In reality, people differ widely in their activity patterns -- some are bursty and others are not. Here we show that, if people differ in their activity patterns, bursty behavior does not always hurt the diffusion, and in fact having some (but not all) of the population be bursty significantly helps diffusion. We prove that maximizing diffusion requires heterogeneous activity patterns across agents, and the overall maximizing pattern of agents' activity times does not involve any Poisson behavior