Collective risks permeate society, triggering social dilemmas in which working toward a common goal is impeded by selfish interests. One such dilemma is mitigating runaway climate change. To study the social aspects of climate-change mitigation, we organized an experimental game and asked volunteer groups of three different sizes to invest toward a common mitigation goal. If investments reached a preset target, volunteers would avoid all consequences and convert their remaining capital into monetary payouts. In the opposite case, however, volunteers would lose all their capital with 50% probability. The dilemma was, therefore, whether to invest one's own capital or wait for others to step in. We find that communicating sentiment and outlook helps to resolve the dilemma by a fundamental shift in investment patterns. Groups in which communication is allowed invest persistently and hardly ever give up, even when their current investment deficits are substantial. The improved investment patterns are robust to group size, although larger groups are harder to coordinate, as evidenced by their overall lower success frequencies. A clustering algorithm reveals three behavioral types and shows that communication reduces the abundance of the free-riding type. Climate-change mitigation, however, is achieved mainly by cooperator and altruist types stepping up and increasing contributions as the failure looms. Meanwhile, contributions from free riders remain flat throughout the game.
From fireflies to cardiac cells, synchronization governs important aspects of nature, and the Kuramoto model is the staple for research in this area. We show that generalizing the model to oscillators of dimensions higher than 2 and introducing a positive feedback mechanism between the coupling and the global order parameter leads to a rich and novel scenario: the synchronization transition is explosive at all even dimensions, whilst it is mediated by a time-dependent, rhythmic, state at all odd dimensions. Such a latter circumstance, in particular, differs from all other time-dependent states observed so far in the model. We provide the analytic description of this novel state, which is fully corroborated by numerical calculations. Our results can, therefore, help untangle secrets of observed time-dependent swarming and flocking dynamics that unfold in three dimensions, and where this novel state could thus provide a fresh perspective for as yet not understood formations.
Trust and trustworthiness form the basis for continued social and economic interactions, and they are also fundamental for cooperation, fairness, honesty, and indeed for many other forms of prosocial and moral behaviour. However, trust entails risks, and building a trustworthy reputation requires effort. So how did trust and trustworthiness evolve, and under which conditions do they thrive? To find answers, we operationalize trust and trustworthiness using the trust game with the trustor's investment and the trustee's return of the investment as the two key parameters. We study this game on different networks, including the complete network, random and scale-free networks, and in the well-mixed limit. We show that in all but one case, the network structure has little effect on the evolution of trust and trustworthiness. Specifically, for well-mixed populations, lattices, random and scale-free networks, we find that trust never evolves, while trustworthiness evolves with some probability depending on the game parameters and the updating dynamics. Only for the scale-free network with degree non-normalized dynamics, we find parameter values for which trust evolves but trustworthiness does not, as well as values for which both trust and trustworthiness evolve. We conclude with a discussion about mechanisms that could lead to the evolution of trust and outline directions for future work.
The divergence between the Pareto distribution and the log-normal distribution has been observed persistently over the past couple of decades in complex network research, economics, and social sciences. To address this, we here propose an approach termed as the accumulative law and its related probability model. We show that the resulting accumulative distribution has properties that are akin to both the Pareto distribution and the log-normal distribution, which leads to a broad range of applications in modelling and fitting real data. We present all the details of the accumulative law, describe the properties of the distribution, as well as the allocation and the accumulation of variables. We also show how the proposed accumulative law can be applied to generate complex networks, to describe the accumulation of personal wealth, and to explain the scaling of internet traffic across different domains.
Synchronization in complex networks is an evergreen subject with numerous applications in biological, social, and technological systems. We here study whether a transition from a single variable to multivariable coupling facilitates the emergence of synchronization in a network of circulant oscillators. We show that the network indeed has much better synchronizability when individual dynamical units are coupled through multiple variables rather than through just one. In particular, we consider in detail four different coupling scenarios for a simple three-dimensional chaotic circulant system, and we determine the smallest coupling strength needed for complete synchronization. We find that the smallest coupling strength is needed when the coupling is through all three variables, and that for the same level of synchronization through a single variable a much stronger coupling strength is needed. Our results thus show that multivariable coupling provides a significantly more efficient synchronization profile in complex networks.