The evolution of lying in well-mixed populations

Lies can have profoundly negative consequences for individuals, groups and even for societies. Understanding how lying evolves and when it proliferates is therefore of significant importance for our personal and societal well-being. To that effect, we here study the sender–receiver game in well-mixed populations with methods of statistical physics. We use the Monte Carlo method to determine the stationary frequencies of liars and believers for four different lie types. We consider altruistic white lies that favour the receiver at a cost to the sender, black lies that favour the sender at a cost to the receiver, spiteful lies that harm both the sender and the receiver, and Pareto white lies that favour both the sender and the receiver. We find that spiteful lies give rise to trivial behaviour, where senders quickly learn that their best strategy is to send a truthful message, while receivers likewise quickly learn that their best strategy is to believe the sender’s message. For altruistic white lies and black lies, we find that most senders lie while most receivers do not believe the sender’s message, but the exact frequencies of liars and non-believers depend significantly on the payoffs, and they also evolve non-monotonically before reaching the stationary state. Lastly, for Pareto white lies we observe the most complex dynamics, with the possibility of both lying and believing evolving with all frequencies between 0 and 1 in dependence on the payoffs. We discuss the implications of these results for moral behaviour in human experiments

Lying on networks: the role of structure and topology in promoting honesty

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

Hierarchical invasion of cooperation in complex networks

The emergence and survival of cooperation is one of the hardest problems still open in science. Several factors such as the existence of punishment, repeated interactions, topological effects and the formation of prestige may all contribute to explain the counter-intuitive prevalence of cooperation in natural and social systems. The characteristics of the interaction networks have been also signaled as an element favoring the persistence of cooperators. Here we consider the invasion dynamics of cooperative behaviors in complex topologies. The invasion of a heterogeneous network fully occupied by defectors is performed starting from nodes with a given number of connections (degree) k0. The system is then evolved within a Prisoner’s Dilemma game and the outcome is analyzed as a function of k0 and the degree k of the nodes adopting cooperation. Carried out using both numerical and analytical approaches, our results show that the invasion proceeds following preferentially a hierarchical order in the nodes from those with higher degree to those with lower degree. However, the invasion of cooperation will succeed only when the initial cooperators are numerous enough to form a cluster from which cooperation can spread. This implies that the initial condition has to be a suitable equilibrium between high degree and high numerosity. These findings have potential applications to the problem of promoting pro-social behaviors in complex networks

Partner selection supported by opaque reputation promotes cooperative behavior

Reputation plays a major role in human societies, and it has been proposed as an explanation for the evolution of cooperation. While the majority of previous studies equates reputation with a transparent and complete history of players' past decisions, in real life, reputations are often ambiguous and opaque. Using web-based experiments, we explore the extent to which opaque reputation works in isolating defectors, with and without partner selection opportunities. Our results show that low reputation works as a signal of untrustworthiness, whereas medium or high reputation are not taken into account by participants for orienting their choices. We also find that reputation without partner selection does not promote cooperative behavior; that is, defectors do not turn into cooperators only for the sake of getting a positive reputation. Finally, in a third study, we find that, when reputation is pivotal to selection, then a substantial proportion of would-be defectors turn into cooperators. Taken together, these results provide insights on the characteristics of reputation and on the way in which humans make use of it when selecting partners but also when knowing that they will be selected

Effects of Mass Media and Cultural Drift in a Model for Social Influence

In the context of an extension of Axelrod's model for social influence, we study the interplay and competition between the cultural drift, represented as random perturbations, and mass media, introduced by means of an external homogeneous field. Unlike previous studies [J. C. Gonz\'alez-Avella {\it et al}, Phys. Rev. E {\bf 72}, 065102(R) (2005)], the mass media coupling proposed here is capable of affecting the cultural traits of any individual in the society, including those who do not share any features with the external message. A noise-driven transition is found: for large noise rates, both the ordered (culturally polarized) phase and the disordered (culturally fragmented) phase are observed, while, for lower noise rates, the ordered phase prevails. In the former case, the external field is found to induce cultural ordering, a behavior opposite to that reported in previous studies using a different prescription for the mass media interaction. We compare the predictions of this model to statistical data measuring the impact of a mass media vasectomy promotion campaign in Brazil.Comment: 10 pages, 3 figures; minor changes; added references. To appear in IJMP

Random Topologies and the emergence of cooperation: the role of short-cuts

We study in detail the role of short-cuts in promoting the emergence of cooperation in a network of agents playing the Prisoner's Dilemma Game (PDG). We introduce a model whose topology interpolates between the one-dimensional euclidean lattice (a ring) and the complete graph by changing the value of one parameter (the probability p to add a link between two nodes not already connected in the euclidean configuration). We show that there is a region of values of p in which cooperation is largely enhanced, whilst for smaller values of p only a few cooperators are present in the final state, and for p \rightarrow 1- cooperation is totally suppressed. We present analytical arguments that provide a very plausible interpretation of the simulation results, thus unveiling the mechanism by which short-cuts contribute to promote (or suppress) cooperation

Freezing and Slow Evolution in a Constrained Opinion Dynamics Model

We study opinion formation in a population that consists of leftists, centrists, and rightist. In an interaction between neighboring agents, a centrist and a leftist can become both centrists or leftists (and similarly for a centrist and a rightist). In contrast, leftists and rightists do not affect each other. The initial density of centrists rho_0 controls the evolution. With probability rho_0 the system reaches a centrist consensus, while with probability 1-rho_0 a frozen population of leftists and rightists results. In one dimension, we determine this frozen state and the opinion dynamics by mapping the system onto a spin-1 Ising model with zero-temperature Glauber kinetics. In the frozen state, the length distribution of single-opinion domains has an algebraic small-size tail x^{-2(1-psi)} and the average domain size grows as L^{2*psi}, where L is the system length. The approach to this frozen state is governed by a t^{-psi} long-time tail with psi-->2*rho_0/pi as rho_0-->0.Comment: 4 pages, 6 figures, 2-column revtex4 format, for submission to J. Phys. A. Revision contains lots of stylistic changes and 1 new result; the main conclusions are the sam

Solution of voter model dynamics on annealed small-world networks

An analytical study of the behavior of the voter model on the small-world topology is performed. In order to solve the equations for the dynamics, we consider an annealed version of the Watts-Strogatz (WS) network, where long-range connections are randomly chosen at each time step. The resulting dynamics is as rich as on the original WS network. A temporal scale $\tau$ separates a quasi-stationary disordered state with coexisting domains from a fully ordered frozen configuration. $\tau$ is proportional to the number of nodes in the network, so that the system remains asymptotically disordered in the thermodynamic limit.Comment: 11 pages, 4 figures, published version. Added section with extension to generic number of nearest neighbor