Modeling opinion misperception and the emergence of silence in online social system.

In the last decades an increasing deal of research has investigated the phenomenon of opinion misperception in human communities and, more recently, in social media. Opinion misperception is the wrong evaluation by community's members of the real distribution of opinions or beliefs about a given topic. In this work we explore the mechanisms giving rise to opinion misperception in social media groups, which are larger than physical ones and have peculiar topological features. By means of numerical simulations, we suggest that the structure of connections of such communities plays indeed a role in distorting the perception of the agents about others' beliefs, but it is essentially an indirect effect. Moreover, we show that the main ingredient that generates misperception is a spiral of silence induced by few, well connected and charismatic agents, which rapidly drives the majority of individuals to stay silent without disclosing their true belief, leading minoritarian opinions to appear more widespread throughout the community.

Gossip and competitive altruism support cooperation in a Public Good game.

When there is an opportunity to gain a positive reputation, individuals are more willing to sacrifice their immediate self-interest. Partner choice creates opportunities for competitive altruism, i.e. individuals compete to be regarded as more generous and to be chosen for future partnerships. Tests of the competitive altruism hypothesis have focused so far on reputation based on direct observation, whereas the role of gossip has not been theoretically and empirically addressed. Partner choice can create an incentive to cooperate and to send truthful messages, but it can also work in the opposite direction. In order to understand the consequences of partner choice on cooperation and gossip, we designed an experimental study in which participants played a sequence of Public Goods games and gossip rounds. In our two treatments, we observed that cooperation increased when there was an opportunity to be selected, but also that cooperators sent more honest messages than defectors, and that this strategy was prevalent in the treatment in which inter-group competition was implemented. We also found evidence that participants detached themselves from the information more often when lying. Taken together, our study fills a theoretical and empirical gap by showing that partner choice increases both cooperation and honesty of gossip. This article is part of the theme issue 'The language of cooperation: reputation and honest signalling'.

Evolutionary advantages of turning points in human cooperative behaviour.

Cooperation is crucial to overcome some of the most pressing social challenges of our times, such as the spreading of infectious diseases, corruption and environmental conservation. Yet, how cooperation emerges and persists is still a puzzle for social scientists. Since human cooperation is individually costly, cooperative attitudes should have been eliminated by natural selection in favour of selfishness. Yet, cooperation is common in human societies, so there must be some features which make it evolutionarily advantageous. Using a cognitive inspired model of human cooperation, recent work Realpe-Gómez (2018) has reported signatures of criticality in human cooperative groups. Theoretical evidence suggests that being poised at a critical point provides evolutionary advantages to groups by enhancing responsiveness of these systems to external attacks. After showing that signatures of criticality can be detected in human cooperative groups composed by Moody Conditional Cooperators, in this work we show that being poised close to a turning point enhances the fitness and make individuals more resistant to invasions by free riders.

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 that 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. Last, 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 occurs 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.

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.

Humans best judge how much to cooperate when facing hard problems in large groups.

We report the results of a game-theoretic experiment with human players who solve problems of increasing complexity by cooperating in groups of increasing size. Our experimental environment is set up to make it complicated for players to use rational calculation for making the cooperative decisions. This environment is directly translated into a computer simulation, from which we extract the collaboration strategy that leads to the maximal attainable score. Based on this, we measure the error that players make when estimating the benefits of collaboration, and find that humans massively underestimate these benefits when facing easy problems or working alone or in small groups. In contrast, when confronting hard problems or collaborating in large groups, humans accurately judge the best level of collaboration and easily achieve the maximal score. Our findings are independent on groups' composition and players' personal traits. We interpret them as varying degrees of usefulness of social heuristics, which seems to depend on the size of the involved group and the complexity of the situation.

Evolution of gossip-based indirect reciprocity on a bipartite network.

Cooperation can be supported by indirect reciprocity via reputation. Thanks to gossip, reputations are built and circulated and humans can identify defectors and ostracise them. However, the evolutionary stability of gossip is allegedly undermined by the fact that it is more error-prone that direct observation, whereas ostracism could be ineffective if the partner selection mechanism is not robust. The aim of this work is to investigate the conditions under which the combination of gossip and ostracism might support cooperation in groups of different sizes. We are also interested in exploring the extent to which errors in transmission might undermine the reliability of gossip as a mechanism for identifying defectors. Our results show that a large quantity of gossip is necessary to support cooperation, and that group structure can mitigate the effects of errors in transmission.

Modeling crowdsourcing as collective problem solving.

Crowdsourcing is a process of accumulating the ideas, thoughts or information from many independent participants, with aim to find the best solution for a given challenge. Modern information technologies allow for massive number of subjects to be involved in a more or less spontaneous way. Still, the full potentials of crowdsourcing are yet to be reached. We introduce a modeling framework through which we study the effectiveness of crowdsourcing in relation to the level of collectivism in facing the problem. Our findings reveal an intricate relationship between the number of participants and the difficulty of the problem, indicating the optimal size of the crowdsourced group. We discuss our results in the context of modern utilization of crowdsourcing.

Social imitation versus strategic choice, or consensus versus cooperation, in the networked Prisoner's Dilemma.

The interplay of social and strategic motivations in human interactions is a largely unexplored topic in collective social phenomena. Whether individuals' decisions are taken in a purely strategic basis or due to social pressure without a rational background crucially influences the model outcome. Here we study a networked Prisoner's Dilemma in which decisions are made either based on the replication of the most successful neighbor's strategy (unconditional imitation) or by pure social imitation following an update rule inspired by the voter model. The main effects of the voter dynamics are an enhancement of the final consensus, i.e., asymptotic states are generally uniform, and a promotion of cooperation in certain regions of the parameter space as compared to the outcome of purely strategic updates. Thus, voter dynamics acts as an interface noise and has a similar effect as a pure random noise; furthermore, its influence is mostly independent of the network heterogeneity. When strategic decisions are made following other update rules such as the replicator or Moran processes, the dynamic mixed state found under unconditional imitation for some parameters disappears, but an increase of cooperation in certain parameter regions is still observed. Comparing our results with recent experiments on the Prisoner's Dilemma, we conclude that such a mixed dynamics may explain moody conditional cooperation among the agents.

Social and strategic imitation: the way to consensus.

Humans do not always make rational choices, a fact that experimental economics is putting on solid grounds. The social context plays an important role in determining our actions, and often we imitate friends or acquaintances without any strategic consideration. We explore here the interplay between strategic and social imitative behavior in a coordination problem on a social network. We observe that for interactions on 1D and 2D lattices any amount of social imitation prevents the freezing of the network in domains with different conventions, thus leading to global consensus. For interactions on complex networks, the interplay of social and strategic imitation also drives the system towards global consensus while neither dynamics alone does. We find an optimum value for the combination of imitative behaviors to reach consensus in a minimum time, and two different dynamical regimes to approach it: exponential when social imitation predominates, power-law when strategic considerations prevail.

Chaos and unpredictability in evolutionary dynamics in discrete time.

A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from those of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace the usual fixed-point population solutions. We observe the familiar period-doubling and chaotic-band-splitting attractor cascades of unimodal maps but in some cases more elaborate variations appear due to bimodality. Also unphysical stationary solutions can have unusual physical implications, such as the uncertainty of the final population caused by sensitivity to initial conditions and fractality of attractor preimage manifolds.

Evolutionary games defined at the network mesoscale: the Public Goods game.

The evolutionary dynamics of the Public Goods game addresses the emergence of cooperation within groups of individuals. However, the Public Goods game on large populations of interconnected individuals has been usually modeled without any knowledge about their group structure. In this paper, by focusing on collaboration networks, we show that it is possible to include the mesoscopic information about the structure of the real groups by means of a bipartite graph. We compare the results with the projected (coauthor) and the original bipartite graphs and show that cooperation is enhanced by the mesoscopic structure contained. We conclude by analyzing the influence of the size of the groups in the evolutionary success of cooperation.

Universality class of triad dynamics on a triangular lattice.

We consider triad dynamics as it was recently considered by Antal [Phys. Rev. E 72, 036121 (2005)] as an approach to social balance. Here we generalize the topology from all-to-all to the regular one of a two-dimensional triangular lattice. The driving force in this dynamics is the reduction of frustrated triads in order to reach a balanced state. The dynamics is parametrized by a so-called propensity parameter p that determines the tendency of negative links to become positive. As a function of p we find a phase transition between different kinds of absorbing states. The phases differ by the existence of an infinitely connected (percolated) cluster of negative links that forms whenever pp(c). From a finite-size scaling analysis we numerically determine the static critical exponents beta and nu(perpendicular) together with gamma, tau, sigma, and the dynamical critical exponents nu(parallel) and delta. The exponents satisfy the hyperscaling relations. We also determine the fractal dimension d(f) that satisfies a hyperscaling relation as well. The transition of triad dynamics between different absorbing states belongs to a universality class with different critical exponents. We generalize the triad dynamics to four-cycle dynamics on a square lattice. In this case, again there is a transition between different absorbing states, going along with the formation of an infinite cluster of negative links, but the usual scaling and hyperscaling relations are violated.

Social balance as a satisfiability problem of computer science.

Reduction of frustration was the driving force in an approach to social balance as it was recently considered by Antal [T. Antal, P. L. Krapivsky, and S. Redner, Phys. Rev. E 72, 036121 (2005)]. We generalize their triad dynamics to k-cycle dynamics for arbitrary integer k. We derive the phase structure, determine the stationary solutions, and calculate the time it takes to reach a frozen state. The main difference in the phase structure as a function of k is related to k being even or odd. As a second generalization we dilute the all-to-all coupling as considered by Antal to a random network with connection probability w<1. Interestingly, this model can be mapped to a satisfiability problem of computer science. The phase of social balance in our original interpretation then becomes the phase of satisfaction of all logical clauses in the satisfiability problem. In common to the cases we study, the ideal solution without any frustration always exists, but the question actually is as to whether this solution can be found by means of a local stochastic algorithm within a finite time. The answer depends on the choice of parameters. After establishing the mapping between the two classes of models, we generalize the social-balance problem to a diluted network topology for which the satisfiability problem is usually studied. On the other hand, in connection with the satisfiability problem we generalize the random local algorithm to a p-random local algorithm, including a parameter p that corresponds to the propensity parameter in the social balance problem. The qualitative effect of the inclusion of this parameter is a bias towards the optimal solution and a reduction of the needed simulation time.

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 quasistationary 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.