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Lying on Networks: the Role of Structure and Topology in Promoting Honesty

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Lying on Networks: the Role of Structure and Topology in Promoting Honesty Middlesex University Research Repository An open access repository of Middlesex University research http://eprints.mdx.ac.uk Capraro, Valerio ORCID: https://orcid.org/0000-0002-0579-0166, Perc, Matjaz and Vilone, Daniele ORCID: https://orcid.org/0000-0002-3485-9249 (2020) Lying on networks: the role of structure and topology in promoting honesty. Physical Review E, 101 (3) , 032305. ISSN 2470-0045 [Article] (doi:10.1103/PhysRevE.101.032305) Final accepted version (with author’s formatting) This version is available at: https://eprints.mdx.ac.uk/29185/ Copyright: Middlesex University Research Repository makes the University’s research available electronically. Copyright and moral rights to this work are retained by the author and/or other copyright owners unless otherwise stated. The work is supplied on the understanding that any use for commercial gain is strictly forbidden. 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See also repository copyright: re-use policy: http://eprints.mdx.ac.uk/policies.html#copy Lying on networks: The role of structure and topology in promoting honesty Valerio Capraro,1, ∗ Matjazˇ Perc,2, 3, 4 and Daniele Vilone5, 6 1Department of Economics, Middlesex University, The Burroughs, London NW4 4BT, U.K. 2Faculty of Natural Sciences and Mathematics, University of Maribor, Koroskaˇ cesta 160, 2000 Maribor, Slovenia 3Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan 4Complexity Science Hub Vienna, Josefstadterstraße¨ 39, 1080 Vienna, Austria 5Laboratory of Agent Based Social Simulation, Institute of Cognitive Science and Technology, National Research Council, Via Palestro 32, 00185 Rome, Italy 6Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matematicas,´ Universidad Carlos III de Madrid, 28911 Leganes,´ Spain Lies can have a negating impact on governments, companies, and the society as a whole. Understanding the dynamics of lying is therefore of crucial importance across different fields of research. While lying has been studied before in well-mixed populations, it is a fact that real interactions are rarely well-mixed. Indeed, they are usually structured and thus best described by networks. Here we therefore use the Monte Carlo method to study the evolution of lying in the sender-receiver game in a one-parameter family of networks, systematically covering complete networks, small-world networks, and one-dimensional rings. We show that lies which benefit the sender at a cost to the receiver, the so-called black lies, are less likely to proliferate on networks than they do in well-mixed populations. Honesty is thus more likely to evolve, but only when the benefit for the sender is smaller than the cost for the receiver. Moreover, this effect is particularly strong in small-world networks, but less so in the one-dimensional ring. For lies that favor the receiver at a cost to the sender, the so-called altruistic white lies, we show that honesty is also more likely to evolve than it is in well-mixed populations. But contrary to black lies, this effect is more expressed in the one-dimensional ring, whereas in small-world networks it is present only when the cost to the sender is greater than the benefit for the receiver. Lastly, for lies that benefit both the sender and the receiver, the so-called Pareto white lies, we show that the network structure actually favors the evolution of lying, but this only when the benefit for the sender is slightly greater than the benefit for the receiver. In this case again the small-world topology acts as an amplifier of the effect, while other network topologies fail to do the same. In addition to these main results we discuss several other findings, which together show clearly that the structure of interactions and the overall topology of the network critically determine the dynamics of lying. I. INTRODUCTION tion [25], have all been successfully studied using methods of physics and the gist of the ‘physics approach’ [33], which is to The conflict between lying and truth-telling is at the core of rationally select the key components of a system until the lat- any social or economic interaction with asymmetric informa- ter is fit to describe the essence of the problem at hand. These tion. Lying, while sometimes interpreted as a sign of intelli- preceding developments certainly invite physics research into gence in children [1] and a relatively common occurrence in the realm of other types of moral behaviors [34], including adults to get out of awkward situations, can be detrimental to lying and honesty [35]. people, governments, organizations, firms, and ultimately to Part of the success of the Monte Carlo method relies on the human societies as a whole. The cost of tax evasions in the fact that it can be used in evolutionary game theory to sim- USA alone, for example, has been estimated at 100 billion per ulate the strategic evolution of the nodes of a network. The year [2]. Lying negatively affects also close personal relation- nodes are occupied by players that interact through a strategic ships, being associated with marital dissatisfaction and friend- game and then, after the accumulation of payoffs, update their ship dissolution [3, 4]. Thus not surprisingly, researchers have strategies through a suitable imitation, replication, or explo- sought to understand factors that determine dishonest behav- ration rule. In fact, this method has proven extremely useful ior for years [5–19]. to study the evolution of cooperation on lattices and heteroge- Here we advance this subject by using methods of statisti- nous networks in social dilemmas [36–41], as well as to study cal physics. Indeed, the past two decades have significantly strategic fairness in the ultimatum game [42–51]. However, to expanded the scope of physics beyond its traditional bound- the best of our knowledge, no previous work has explored the aries. Various aspects of economics [20] and social sciences evolution of honesty and lying on networks. [21–25] have benefited from the Monte Carlo method [26, 27] Here we make a first step in this direction. As a relatively and the coming-of-age of network science [28–31]. In partic- simple but complete mathematical model of lying, we use the ular the social dynamics in general [21], as well as more spe- sender-receiver game [16, 52]. As we will show in the Math- cific aspects of modern human societies, such as crime [22], ematical model section, this paradigm is fundamentally dif- gossiping [32], epidemics [23], vaccination [24], and coopera- ferent from previous games studied using the Monte Carlo method, such as the prisoner’s dilemma and the ultimatum game. At the same time, it is particularly suitable for the application of the Monte Carlo method, and it allows us to ∗Electronic address: [email protected] study the evolution of four different types of lies. Namely, 2 black lies, altruistic white lies, Pareto white lies, and spiteful off of the receiver; the second component that of the sender. lies (the Mathematical model section has all the definitions). The sender privately rolls a six-face dice and looks at the out- While we have previously studied the evolution of lying us- come. Then the sender chooses a message to send to the re- ing the sender-receiver game in well-mixed populations [35], ceiver among six possible messages: “The outcome was i”, it remains an open question whether and to what degree the with i 2 f1; 2; 3; 4; 5; 6g. After receiving the message, the re- fact that our interactions are commonly structured rather than ceiver guesses the true outcome of the roll of the dice. If the well-mixed impacts the results. The evolution of lying in well- receiver guesses the true outcome, then Option A is imple- mixed populations was found to be strongly dependent on the mented as a payment; if the receiver does not guess the true type of lie, and it also displayed complex character that pre- outcome of the roll of the dice, then Option B is implemented. cluded generalizations over different parameters of the game. Therefore, the sender has essentially two strategies: he ei- Since human interactions are not random, as we are more ther sends a truthful message, or not. Similarly, the receiver likely to interact within our social circles, such as with family, has essentially two strategies: she either believes the message friends, or within our workplace with colleagues and cowork- sent by the sender, or not. If the receiver believes the sender, ers, it is thus important to go beyond well-mixed populations she reports the same number as the one sent by the sender; oth- and to study the evolution of lying in networks. erwise, if the receiver does not believe the sender, she draws To that effect, we study the evolution of lying in a large fam- randomly a number from the remaining five numbers of the ily of networks, known as LASW networks [53].
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