# 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. Till date, researchers have mostly focussed on either building such systems by using existing underlying social networks (exogenously built) or on studying quality of service related issues. 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, which is more intuitive than exogenous social networks. 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, 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 analyse the social storage network game. Second, we propose the concept of *bilateral stability* which refines the pairwise stability concept defined by Jackson and Wolinsky (J Econ Theory 71(1):44–74, 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. The notion of *bilateral stability* subsumes the bilateral equilibrium definition of Goyal and Vega-Redondo (J Econ Theory 137(1):460–492, 2007). 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.

## Keywords

Social storage Endogenous network formation Bilateral stability Pairwise stability F2F backup system Peer-to-peer system## Notes

### Acknowledgements

The authors would like to thank the anonymous referees and the editors of this volume for their valuable comments.

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