Learning in Networks: a survey

This paper presents a survey of research on learning with a special focus on the structure of interaction between individual entities. The structure is formally modelled as a network: the nodes of the network are individuals while the arcs admit a variety of interpretations (ranging from information channels to social and economic ties). I first examine the nature of learning about optimal actions for a given network architecture. I then discuss learning about optimal links and actions in evolving networks.

Keeping up with the neighbours: social interaction in a market economy

We consider a world in which individuals have private endowments and trade in markets, while their utility is sensitive to the consumption of their neighbors. Our interest is in understanding how social structure of comparisons, taken together with the familiar fundamentals of the economy � endowments, technology and preferences � shapes equilibrium prices, allocations and welfare. We find that equilibrium prices and allocations depend on average individual centrality in the social network. As we add links to a social network, the centralities rise and this pushes up prices of the socially sensitive good. Newly linked agents demand more of the socially sensitive good, while the reverse happens with regard to the standard good. We derive a formula to compute the critical link, i.e., the new link which maximizes price increase. We then turn to a model with heterogenous endowments, and find that inequality in network centrality and in wealth inequality reinforce each other. Thus a transfer of resources from less to more central agents raises prices of the socially sensitive good and alters allocations and utilities of all agents. We show by example that poor individuals lose utility while rich individuals gain utility as society moves from segregation to integration.

Network Multipliers and the Optimality of Indirect Communication

We study the problem of a firm M which wishes to inform a community of individuals about its product. Information travels within the community because of the social interactions between individuals. Our interest is in understanding how the firm can incorporate the network of social interactions in the design of its communication strategy. We study a model of undirected networks and start by showing that social interactions appear in the payoff of the firm in the form of a network multiplier. We establish that the network multiplier is an increasing function of both the mean and the variance in the distribution of connections of the network. This implies in particular that denser and more dispersed degree distributions are better for the firm. We then show that the degree distribution of the neighbour first order dominates the degree distribution of a node at large and so it is always better for a firm to use indirect communication, i.e., viz. picking the neighbour of a node rather than a node itself as the target of communication. Finally, we show that the advantages of indirect communication are increasing with dispersion in the degree distribution.

A Theory of Strategic Diffusion

The important role of friends, neighbors and colleagues in shaping individual choices has been brought out in a number of studies over the years. The presence of significant ‘local’ influence in shaping individual behavior suggests that firms, governments and developmental agencies should explicitly incorporate it in the design of their marketing and developmental strategies. This paper develops a framework for the study of optimal strategies in the presence of social interaction. We focus on the case of a single player who exerts costly effort to get a set of individuals – engaged in social interaction – to choose a certain action. Our formulation allows for different types of social interaction (ranging from sharing of information to direct adoption externalities) and also allows for the player to have incomplete information concerning the connections among individuals. The analysis starts by showing that incorporating information on social interaction can have large effects on the profits of a player. We then show that an increase in the level and dispersion of social interaction can raise or lower the optimal strategy and profits of the player, depending on the content of the interaction. We then study the value of social network information for the player and find that it depends on the dispersion in social connections. The economic interest of these results is illustrated via a discussion of two economic applications: advertising in the presence of word of mouth communication and seeding a network.Social Interaction, Seeding the Network, Word of Mouth Communication, Diffusion Strategy

Favoritism

Favoritism is the act of offering jobs, contracts and resources to members of one's social group in preference to outsiders. Favoritism is widely practiced and this motivates an exploration of its origins and economic consequences. Our main finding is that individuals have an interest to trade favors over time and that this will come at the expense of others, who are outside their group. We show that favoritism is relatively easier to sustain in smaller groups. Favoritism entails social costs as it usually leads to inefficient allocations. However, favoritism can lead to payoff advantages for larger groups. Productivity enhancing investments are larger in groups which practice favoritism. The availability of investment opportunities can reinforce payoff inequalities across groups.Favoritism, nepotism, reciprocity, repeated games

A Theory of Strategic Diffusion

The important role of friends, neighbors and colleagues in shaping individual choices has been brought out in a number of studies over the years. The presence of significant 'local' influence in shaping individual behavior suggests that firms, governments and developmental agencies should explicitly incorporate it in the design of their marketing and developmental strategies. This paper develops a framework for the study of optimal strategies in the presence of social interaction. We focus on the case of a single player who exerts costly effort to get a set of individuals � engaged in social interaction � to choose a certain action. Our formulation allows for different types of social interaction and also allows for the player to have incomplete information concerning the connections among individuals. We first show that incorporating information on social interaction can have large effects on the profits of a player. Then, we establish that an increase in the level and dispersion of social interaction can raise or lower the optimal strategy and profits of the player, depending on the content of the interaction. Finally, we study the value of social network information for the player and find that it depends on the dispersion in social connections. The economic interest of these results is illustrated via a discussion of two economic applications: advertising in the presence of word of mouth communication and seeding a network.

Favoritism

Favoritism is the act of offering jobs, contracts and resources to members of one's social group in preference to outsiders. Favoritism is widely practiced and this motivates an exploration of its origins and economic consequences. Our main finding is that individuals have an interest to trade favors over time and that this will come at the expense of others, who are outside their group. We show that favoritism is relatively easier to sustain in smaller groups. Favoritism entails social costs as it usually leads to inefficient allocations. However, favoritism can lead to payoff advantages for larger groups. Productivity enhancing investments are larger in groups which practice favoritism. The availability of investment opportunities can reinforce payoff inequalities across groups

Network Formation and Social Coordination

This paper develops a simple model to examine the interaction between partner choice and individual behavior in games of coordination. An important ingredient of our approach is the way we model partner choice: we suppose that a player can establish ties with other players by unilaterally investing in costly pair-wise links. In this context, individual efforts to balance the costs and benefits of links are shown to lead to a unique equilibrium interaction architecture. The dynamics of network formation, however, has powerful effects on individual behavior: if costs of forming links are below a certain threshold then players coordinate on the risk-dominant action, while if costs are above this threshold then they coordinate on the efficient action. These findings are robust to a variety of modifications in the link formation process. For example, it may be posited that, in order for a link to materialize, the link proposal must be two-sided (i.e. put forward by both agents); or that, in case of a unilateral proposal, the link may be refused by the other party (if, say, the latter's net payoff is negative); or that a pair of agents can play the game even if connected only through indirect links.Networks, Links, Coordination games, Equilibrium selection, Risk dominance, Efficiency