  The viral propagation of fake posts on online social networks (OSNs) has
become an alarming concern. The paper aims to design control mechanisms for
fake post detection while negligibly affecting the propagation of real posts.
Towards this, a warning mechanism based on crowd-signals was recently proposed,
where all users actively declare the post as real or fake. In this paper, we
consider a more realistic framework where users exhibit different adversarial
or non-cooperative behaviour: (i) they can independently decide whether to
provide their response, (ii) they can choose not to consider the warning signal
while providing the response, and (iii) they can be real-coloring adversaries
who deliberately declare any post as real. To analyze the post-propagation
process in this complex system, we propose and study a new branching process,
namely total-current population-dependent branching process with multiple death
types. At first, we compare and show that the existing warning mechanism
significantly under-performs in the presence of adversaries. Then, we design
new mechanisms which remarkably perform better than the existing mechanism by
cleverly eliminating the influence of the responses of the adversaries.
Finally, we propose another enhanced mechanism which assumes minimal knowledge
about the user-specific parameters. The theoretical results are validated using
Monte-Carlo simulations.
