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Rumor Spreading and Source Identification: A Hide and Seek Game

The goal of a rumor source node in a social network is to spread its rumor to as many nodes as possible, while remaining hidden from the network administrator. On the other hand, the network administrator aims to identify the source node based on knowledge of which nodes have accepted the rumor (which are called infected nodes). We model the rumor spreading and source identification problem as a strategic game, where the rumor source and the network administrator are the two players. As the Jordan center estimator is a minimax source estimator that has been shown to be robust in recent works, we assume that the network administrator utilizes a source estimation strategy that probes every node within a given radius of the Jordan center. Given any estimation strategy, we design a best-response infection strategy for the rumor source. Given any infection strategy, we design a best-response estimation strategy for the network administrator. We derive conditions under which the Nash equilibria of the strategic game exist. Simulations in both synthetic and real-world networks demonstrate that our proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.