Stability, Efficiency, and Contentedness of Social Storage Networks

Abstract: Social storage systems are a good alternative to existing data backup systems of local, centralized, and P2P backup. In this paper, we look at two untouched aspects of social storage systems. One aspect involves modelling social storage as an endogenous social network, where agents themselves decide with whom they want to build data backup relation. The second aspect involves studying the stability of social storage systems, which would help reduce maintenance costs and further, help build efficient as well as contented networks. We have a four fold contribution that covers the above two aspects. We, first, model the social storage system as a strategic network formation game. We define the utility of each agent in the network under two different frameworks. Second, we propose the concept of bilateral stability which refines the pairwise stability concept defined by Jackson et. al. 1996, by requiring mutual consent for both addition and deletion of links, as compared to mutual consent just for link addition. Mutual consent for link deletion is especially important in the social storage setting. Third, we prove necessary and the sufficient conditions for bilateral stability of social storage networks. For symmetric social storage networks, we prove that there exists a unique neighborhood size, independent of the number of agents (for all non-trivial cases), where no pair of agents has any incentive to increase or decrease their neighborhood size. We call this neighborhood size as the stability point. Fourth, given the number of agents and other parameters, we discuss which bilaterally stable networks would evolve and also discuss which of these stable networks are efficient --- that is, stable networks with maximum sum of utilities of all agents. We also discuss ways to build contented networks, where each agent achieves the maximum possible utility.