Unique Stability Point in Social Storage Networks

We model social storage systems as a strategic network formation game. We define the utility of each player in the network under two different frameworks, one where the cost to add and maintain links is considered in the utility function and the other where budget constraints are considered. In the context of social storage and social cloud computing, these utility functions are the first of its kind, and we use them to define and analyze the social storage network game. We, then, present the pairwise stability concept adapted for social storage where both addition and deletion of links require mutual consent, as compared to mutual consent just for link addition in the pairwise stability concept defined by Jackson and Wolinsky [35]. Mutual consent for link deletion is especially important in the social storage setting. For symmetric storage networks, we prove that there exists a unique neighborhood size, independent of the number of players, where no pair of users has any incentive to increase or decrease their neighborhood size. We call this neighborhood size as the stability point. We provide some necessary and sufficient conditions for pairwise stability of social storage networks. Further, given the number of players and other parameters, we discuss which pairwise stable networks would evolve. We also show that in a connected pairwise stable network there can be at most one player with neighborhood size one less than (or one more than) the stability point.