Can the indifferent population affect the spread of rumors?
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abstract
In this work we intend to answer the question of the title, a question that arises from reading the work of Accinelli, Muñiz and Quintas (2023) [3]. In this work, we study a repeated game and replicator dynamics to analyze the spread of a rumor in a society where individuals of three different types or subpopulations coexist. A group of individuals, informed or not about the true content of a rumor, are interested in transmitting it but not always with the original content, some will prefer to distort it or modify its content, while a third group will be indifferent to the content of the rumor in the sense that they do not have great interest in disseminating it, which does not prevent them from transmitting it once the rumor is known. We conclude that there are three possibilities for the spread of a rumor. The rumor end up being disseminated, either in its original or distorted version by all those interested in its content, or a part of the population will remain in the long term spreading the rumor in its original form and another in a distorted form. We will see that this situation will not be stable and it can only be maintained if the population is originally distributed in this way, which corresponds to a Nash equilibrium in mixed strategies. We will show that the group of indifferent affects not only the speed with which the rumor spreads, regardless of the veracity of its content, but also to the population distribution corresponding to the Nash equilibrium.
