Signaling in social network and social capital formation

This paper presents a model of social capital and social network formation. The key interaction within the model is that whom an individual chooses to become friends with affects the value (social capital) of the friendship. In the model, how a player searches for and then forms friendships reveals how willing she is to engage in cooperation with a potential friend. Individuals observe their local network structure (friends and cliques) and the actions of players within these. Willingness to cooperate is private information and is captured by the discount factor of an individual. Cooperative types have high discount factors and can signal their type by forming a clique through befriending a friend of a friend. Uncooperative types do not form these kinds of friendships because of the local observability of their actions to all members of a clique. Thus, when a player meets someone with whom she shares a friend, her belief that the individual has a high discount factor is greater than the population average. In this sense, people “trust” each other more when they share a friend in common. Finally, I relate the primitives of the model to characteristics of the implied social network by nesting the sequential equilibrium in an algorithm of network formation proposed by Jackson and Rogers (Am Econ Rev 97(3):890–915, 2007). The model highlights a trade-off between maximizing the total amount of social capital in a society and distributing it equitably across individuals.