Abstract
In this paper, we consider a novel game theory model for the competitive influence maximization problem. We model this problem as a simultaneous non-cooperative game with complete information and rational players, where there are at least two players who are supposed to be out of the network and are trying to institutionalize their options in the social network; that is, the objective of players is to maximize the spread of a desired opinion rather than the number of infected nodes. In the proposed model, we extend both the Linear Threshold model and the Independent Cascade model. We study an influence maximization model in which users’ heterogeneity, information content, and network structure are considered. Contrary to previous studies, in the proposed game, players find not only the most influential initial nodes but also the best information content. The proposed novel game was implemented on a real data set where individuals have different tendencies toward the players’ options that change over time because of gaining influence from their neighbors and the information content they receive. This means that information content, the topology of the graph, and the individual’s initial tendency significantly affect the diffusion process. The proposed game is solved and the Nash equilibrium is determined for a real data set. Lastly, the numerical results obtained from the proposed model were compared with some well-known models previously reported in the literature.
Highlights
In recent years, there has been a growing interest in studying social networks as they have widespread application in different fields such as sociology, economics, computer science, biology, and mathematics [1,2,3,4,5,6]
It is thought that diffusion of messages is usually more effective and convincing if messages are received from a friend rather than from a social change agent [9]
Most studies have been focused on a situation in which players attempt to find the most influential nodes in order to maximize the total number of infected nodes at the end of the diffusion process [5,7,8]
Summary
There has been a growing interest in studying social networks as they have widespread application in different fields such as sociology, economics, computer science, biology, and mathematics [1,2,3,4,5,6]. While the previous studies assumed that players only aim to find the most influential initial nodes, in the model developed here players have the additional goal of finding the best message content To this end, it is assumed that social change agents attempt to maximize the total sum of the tendencies of individuals toward their own diffused options rather than maximizing the total number of infected nodes. In the current paper, a node is called active if there is a received message that can change its own tendency, and players seek to maximize the sum of individuals’ tendencies toward their options, i.e., the level of society’s desire to choose the options taken by the players is maximized All of these considerations bring the proposed model closer to reality compared to previous studies.
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