Abstract
We study a sequential Bayesian persuasion game in which two news senders having opposite preferences over two alternatives try to persuade voters. The first mover's informative news can be fabricated by the second mover's uninformative news, and either news is randomly transmitted to and received by voters who do not know its genuine source. We construct equilibrium strategies by introducing a novel method using a Rothschild-Stiglitz approach. We find that there are two types of equilibrium outcomes, which depend on the probability that the voters are exposed to the second sender's news -- which we call the prevalence of fake news. When the prevalence of fake news is low, the first sender produces more accurate news as the prevalence of fake news increases, thereby improving the voters' information surplus. However, when the prevalence of fake news is high, the informativeness of the first sender's news deteriorates by the second sender's fabrication and thus the value of the news is reduced to zero. Our analysis explains an incentive of fake news production and its effect on the quality of the news transmitted via social media, where the source of news is hardly identifiable.
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