Abstract
Inspired by the Daley-Kendall and Goffman-Newill models, we propose an Ignorant-Believer-Unbeliever rumor (or fake news) spreading model with the following characteristics: (i) a network contact between individuals that determines the spread of rumors; (ii) the value (cost versus benefit) for individuals who search for truthful information (learning); (iii) an impact measure that assesses the risk of believing the rumor; (iv) an individual search strategy based on the probability that an individual searches for truthful information; (v) the population search strategy based on the proportion of individuals of the population who decide to search for truthful information; (vi) a payoff for the individuals that depends on the parameters of the model and the strategies of the individuals. Furthermore, we introduce evolutionary information search dynamics and study the dynamics of population search strategies. For each value of searching for information, we compute evolutionarily stable information (ESI) search strategies (occurring in non-cooperative environments), which are the attractors of the information search dynamics, and the optimal information (OI) search strategy (occurring in (eventually forced) cooperative environments) that maximizes the expected information payoff for the population. For rumors that are advantageous or harmful to the population (positive or negative impact), we show the existence of distinct scenarios that depend on the value of searching for truthful information. We fully discuss which evolutionarily stable information (ESI) search strategies and which optimal information (OI) search strategies eradicate (or not) the rumor and the corresponding expected payoffs. As a corollary of our results, a recommendation for legislators and policymakers who aim to eradicate harmful rumors is to make the search for truthful information free or rewarding.
Highlights
The theory of rumor spreading proposed by Daley and Kendall [1,2] became known as the DK model, in which a population is divided into three different groups: ignorants—people who are ignorant concerning the rumor; spreaders—people who actively spread the rumor; and stiflers—people who have heard the rumor but are no longer interested in spreading it
For rumors that are harmful to the population, we show the existence of three distinct scenarios that occur, depending on the value of searching for truthful information: (i) for positive values of searching, both evolutionarily stable information (ESI) and optimal information (OI) search strategies coincide, and all individuals search for truthful information, eradicating the rumor; (ii) for small negative values of searching, the OI
By Lemma 3 and Remark 2, (i) for small values of the information search v ≤ W, the optimal strategy sO = 0 coincides with the evolutionarily stable information search strategy s ESI = 0, in which individuals never search for truthful information; (ii) for positive values of the information search v ≥ W, the optimal strategy sO = 1 coincides with the evolutionarily stable information search strategy s ESI = 1, in which individuals always search for truthful information
Summary
The theory of rumor (or fake news) spreading proposed by Daley and Kendall [1,2] became known as the DK model, in which a population is divided into three different groups: ignorants—people who are ignorant concerning the rumor; spreaders—people who actively spread the rumor; and stiflers—people who have heard the rumor but are no longer interested in spreading it. We introduce the expected information search payoff, which depends on (i) his/her information search strategy S; (ii) the population information search strategy s; (iii) the value v of searching for truthful information; (iv) the impact measure y of the rumor; and (v) the spread dynamics of the rumor. We fully characterize the triples (v, y, S), where S is (i) a Nash strategy, (ii) an evolutionarily stable information search strategy, or (iii) an optimal information search strategy; v is the value of searching for information; and y is the impact measure of believing a false rumor (fake news). For rumors that are advantageous to the population (positive impact y > 0), three distinct scenarios occur, depending on the value of searching for truthful information: (i) for high positive values of searching, both evolutionarily stable information (ESI) and optimal information (OI).
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