Stability and Efficiency of Social Networks with Strategic, Resource Constrained Nodes

Recently, the topic of social network formation has received significant attention since the structure of the networks has a profound impact on the economic outcomes in many real world applications such as large exchange markets, sponsored search auctions, and viral marketing. Stability and efficiency are two important properties which are sought in such networks. These two properties are both desirable but not always compatible. This paper investigates the tradeoff between stability and efficiency in a noncooperative game model of social network formation. In our model, we consider network formation in which each node can form at most k links due to scarcity of the resources. We formulate the network formation process as a strategic form game.We view the notion of stability as obtaining a Nash equilibrium outcome and efficiency as maximizing the value of the network. In this setting, we show that all efficient networks are stable in both the cases: (i) k = 1 and (ii) k = 2.