How good is the Shapley value-based approach to the influence maximization problem?

This paper studies the process of information diffusion over a network, where new nodes as time passes become “informed” (or equivalently, influenced or infected), and a related problem of influence maximization that concerns finding the set of initial nodes that will lead to the most widespread effect of diffusion in the network [4, 6]. Influence maximization is an NP-hard problem [4], and therefore, literature has focused on approximating the optimal solution with greedy algorithms and various heuristics [4, 2, 3]. In this spirit, recent research [5, 1] proposed the Shapley value, a concept borrowed from game theory, as a measure of node centrality. The key idea is to define a cooperative game over a network in which players are nodes, coalitions are groups of nodes, and payoffs of coalitions depend on how many nodes these coalitions can infect as a group. Next, a game-theoretic solution concept—most often the Shapley value—quantifies a role or importance of a player (e.g. in the diffusion process) by its average marginal contribution in the game. In this paper, we also briefly test the Banzhaf index (BI) as an alternative solution concept. Nevertheless, unlike other centrality measures, the game-theoretic centrality for influence maximization has not been yet rigorously evaluated. The only experimental work is that of Ramasuri and Narahari [5] who proposed the SPIN algorithm built upon the Shapley value. This evaluation is, however, very preliminary, as it relies on the approximated Shapley value and is not scalable even for the graphs larger than 15K nodes Chen et al. [2]. In this paper, we firstly correct the above shortcomings building upon the work of Aadithya et al. [1]. We further show that the use of the Shapley value is not restricted to those games and propose the use of the Shapley value in the LDAG model from Chen et al. [2]. Finally, we verify the usefulness of the algorithms in [1] in information diffusion application and compare it against current state-of-the art algorithms for estimation of top k nodes.