Strategies for utility maximization in social groups with preferential exploration

摘要

Social Group is group of interconnected nodes interested in obtaining common content (Scott, in Social network analysis, 2012). Social groups are observed in many networks for example, cellular network assisted Device-to-Device network (Fodor et al., in IEEE Commun Mag 50:170–177, 2012, Lei et al., in Wirel Commun 19:96–104, 2012), hybrid Peer-to-Peer content distribution (Christos Gkantsidis and Miller, in 5th International Workshop on Peer-to-Peer Systems, 2006, Vakali and Pallis, in IEEE Internet Comput 7:68–74, 2003) etc. In this paper, we consider a “Social Group” of networked nodes, seeking a “universe” of data segments for maximizing their individual utilities. Each node in social group has a subset of the universe, and access to an expensive link for downloading data. Nodes can also acquire the universe by exchanging copies of data segments among themselves, at low cost, using inter-node links. While exchanges over inter-node links ensure minimum or negligible cost, some nodes in the group try to exploit the system by indulging in collusion, identity fraud etc. We term such nodes as ‘non-reciprocating nodes’ and prohibit such behavior by proposing the “Give-and-Take” criterion, where exchange is allowed iff each participating node provides at least one segment to the node which is unavailable with the node. While complying with this criterion, each node wants to maximize its utility, which depends on the node’s segment set available with the node. Link activation between pair of nodes requires mutual consent of the participating nodes. Each node tries to find a pairing partner by preferentially exploring nodes for link formation. Unpaired nodes download data segments using the expensive link with pre-defined probability (defined as segment aggressiveness probability). We present various linear complexity decentralized algorithms based on the Stable Roommates Problem that can be used by nodes for choosing the best strategy based on available information. We present a decentralized randomized algorithm that is asymptotically optimal in the number of nodes. We define Price of Choice for benchmarking the performance of social groups consisting of non-aggressive nodes (i.e. nodes not downloading data segments from the expensive link) only. We evaluate performances of various algorithms and characterize the behavioral regime that will yield best results for nodes and social groups, spending the least on the expensive link. The proposed algorithms are compared with the optimal. We find that the Link For Sure algorithm performs nearly optimally.