Single-out fake posts: participation game and its design

Crowd-sourcing models, which leverage the collective opinions/signals of users on online social networks (OSNs), are well-accepted for fake post detection; however, motivating the users to provide the crowd signals is challenging, even more so in the presence of adversarial users. We design a participation (mean-field) game where users of the OSN are lured by a reward-based scheme to provide the binary (real/fake) signals such that the OSN achieves $(\theta, \delta)$-level of actuality identification (AI) - not more than $\delta$ fraction of non-adversarial users incorrectly judge the real post, and at least $\theta$ fraction of non-adversarial users identify the fake post as fake. An appropriate warning mechanism is proposed to influence the decision-making of the users such that the resultant game has at least one Nash Equilibrium (NE) achieving AI. We also identify the conditions under which all NEs achieve AI. Further, we numerically illustrate that one can always design an AI game if the normalized difference in the innate identification capacities of the users is at least $1\%$, when desired $\theta = 75\%$.