Networks of Relations and Social Capital

Internet peering as a network of relations

“…Strategy profile 1 is an equilibrium as long the sum of the net gains of each player's for all his relations is positive. This implies the following result shown in LS [19]: For an environment with perfect transmission of information on the history of any player in the network, if each of the bilateral relations is such that due to an asymmetry in the payoffs, one player has a positive net gain from cooperation and the other has a negative one, then, absent transfers, 1. cooperation in non-circular networks, i.e. in lines, stars, or other forms of trees, is not sustainable because of an "end-network effect" analogous to "end game effects" in finally repeated games;…”

“…LS [19] show that if players repeatedly interact in bilateral prisoners' dilemmas with asymmetric gains from cooperation, they may cooperate for a larger range of discount factors, if they are able to pool payoff asymmetries in a multilateral punishment mechanism. Consider figure 5, which represents the normal form of a generic prisoners' dilemma, in which c i stands for the cooperation payoff, d i for the payoff if both d efect, b i stands for the payoff player i gets if he betrays while the other player cooperates, and l i stands for the l oss payoff if player i is betrayed while cooperating.…”

“…In this section, we will first briefly discuss some theoretical results in Lippert and Spagnolo 6 [19] (from here on LS) and then apply them to shed some light on when and how the network structure of peering relationships among ISPs may substantially reduce the problem of asymmetry in bilateral relations. We will finally show that introducing bilateral paid peering is only an imperfect substitute for making use of the network structure of the peering relationships.…”

“…However, in this paper, we are not dealing with network formation but with the enforceability of implicit cooperative agreements in dynamic settings within an existing network. To our knowledge, for this purpose, the closest reference is Lippert and Spagnolo [19] Player 1…”

Local Network Effects and Complex Network Structure

“…Jackson and Rogers (2004) analyze a dynamic model of network formation with costly search which explains when networks with low inter-vertex distances and a high degree of clustering ("small-world networks") and those with power-law degree distributions are likely to form. Lippert and Spagnolo (2004) analyze the structure of networks of inter-agent relations, which could form the basis for an underlying social network.…”