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We study the evolution of cooperation in the collective-risk social dilemma game, where the risk is determined by a collective target that must be reached with individual contributions. All players initially receive endowments from the available amount of common resources. While cooperators contribute part of their endowment to the collective target, defectors do not. If the target is not reached, the endowments of all players are lost. In our model, we introduce a feedback between the amount of common resources and the contributions of cooperators. We show that cooperation can be sustained only if the common resources are preserved but never excessively abound. This, however, requires a delicate balance between the amount of common resources that initially exist, and the amount cooperators contribute to the collective target. Exceeding critical thresholds in either of the two amounts leads to loss of cooperation, and consequently to the depletion of common resources.

Research has shown that the addition of abstention as an option transforms social dilemmas to rock-paper-scissor type games, where defectors dominate cooperators, cooperators dominate abstainers (loners), and abstainers (loners), in turn, dominate defectors. In this way, abstention can sustain cooperation even under adverse conditions, although defection also persists due to cyclic dominance. However, to abstain or to act as a loner has, to date, always been considered as an independent, third strategy to complement traditional cooperation and defection. Here we consider probabilistic abstention, where each player is assigned a probability to abstain in a particular instance of the game. In the two limiting cases, the studied game reverts to the prisoner's dilemma game without loners or to the optional prisoner's dilemma game. For intermediate probabilities, we have a new hybrid game, which turns out to be most favorable for the successful evolution of cooperation. We hope this novel hybrid game provides a more realistic view of the dilemma of optional/voluntary participation.

The World Health Organization declared the coronavirus disease 2019 a pandemic on March 11th, pointing to the over 118,000 cases in over 110 countries and territories around the world at that time. At the time of writing this manuscript, the number of confirmed cases has been surging rapidly past the half-million mark, emphasizing the sustained risk of further global spread. Governments around the world are imposing various containment measures while the healthcare system is bracing itself for tsunamis of infected individuals that will seek treatment. It is therefore important to know what to expect in terms of the growth of the number of cases, and to understand what is needed to arrest the very worrying trends. To that effect, we here show forecasts obtained with a simple iteration method that needs only the daily values of confirmed cases as input. The method takes into account expected recoveries and deaths, and it determines maximally allowed daily growth rates that lead away from exponential increase toward stable and declining numbers. Forecasts show that daily growth rates should be kept at least below 5% if we wish to see plateaus any time soon—unfortunately far from reality in most countries to date. We provide an executable as well as the source code for a straightforward application of the method on data from other countries.

We study the evolution of cooperation in the spatial prisoner's dilemma game where players are allowed to establish new interactions with others. By employing a simple coevolutionary rule entailing only two crucial parameters, we find that different selection criteria for the new interaction partners as well as their number vitally affect the outcome of the game. The resolution of the social dilemma is most probable if the selection favors more successful players and if their maximally attainable number is restricted. While the preferential selection of the best players promotes cooperation irrespective of game parametrization, the optimal number of new interactions depends somewhat on the temptation to defect. Our findings reveal that the "making of new friends" may be an important activity for the successful evolution of cooperation, but also that partners must be selected carefully and their number limited.

Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even though their payoffs may be marginally different than those of the other players. Inspired by this observation, we introduce an aspiration-based win-stay-lose-learn strategy updating rule into the spatial prisoner's dilemma game. The rule is simple and intuitive, foreseeing strategy changes only by dissatisfied players, who then attempt to adopt the strategy of one of their nearest neighbors, while the strategies of satisfied players are not subject to change. We find that the proposed winstay-lose-learn rule promotes the evolution of cooperation, and it does so very robustly and independently of the initial conditions. In fact, we show that even a minute initial fraction of cooperators may be sufficient to eventually secure a highly cooperative final state. In addition to extensive simulation results that support our conclusions, we also present results obtained by means of the pair approximation of the studied game. Our findings continue the success story of related winstay strategy updating rules, and by doing so reveal new ways of resolving the prisoner's dilemma.

Corruption crimes demand highly coordinated actions among criminal agents to succeed. But research dedicated to corruption networks is still in its infancy and indeed little is known about the properties of these networks. Here we present a comprehensive investigation of corruption networks related to political scandals in Spain and Brazil over nearly three decades. We show that corruption networks of both countries share universal structural and dynamical properties, including similar degree distributions, clustering and assortativity coefcients, modular structure, and a growth process that is marked by the coalescence of network components due to a few recidivist criminals. We propose a simple model that not only reproduces these empirical properties but reveals also that corruption networks operate near a critical recidivism rate below which the network is entirely fragmented and above which it is overly connected. Our research thus indicates that actions focused on decreasing corruption recidivism may substantially mitigate this type of organized crime.

Corruption crimes demand highly coordinated actions among criminal agents to succeed. But research dedicated to corruption networks is still in its infancy and indeed little is known about the properties of these networks. Here we present a comprehensive investigation of corruption networks related to political scandals in Spain and Brazil over nearly three decades. We show that corruption networks of both countries share universal structural and dynamical properties, including similar degree distributions, clustering and assortativity coefficients, modular structure, and a growth process that is marked by the coalescence of network components due to a few recidivist criminals. We propose a simple model that not only reproduces these empirical properties but reveals also that corruption networks operate near a critical recidivism rate below which the network is entirely fragmented and above which it is overly connected. Our research thus indicates that actions focused on decreasing corruption recidivism may substantially mitigate this type of organized crime.

In the summer of 2021, European governments removed most NPIs after experiencing prolonged second and third waves of the COVID-19 pandemic. Most countries failed to achieve immunization rates high enough to avoid resurgence of the virus. Public health strategies for autumn and winter 2021 have ranged from countries aiming at low incidence by re-introducing NPIs to accepting high incidence levels. However, such high incidence strategies almost certainly lead to the very consequences that they seek to avoid: restrictions that harm people and economies. At high incidence, the important pandemic containment measure 'test-trace-isolate-support' becomes inefficient. At that point, the spread of SARS-CoV-2 and its numerous harmful consequences can likely only be controlled through restrictions. We argue that all European countries need to pursue a low incidence strategy in a coordinated manner. Such an endeavour can only be successful if it is built on open communication and trust. ; peer-reviewed

In the summer of 2021, European governments removed most NPIs after experiencing prolonged second and third waves of the COVID-19 pandemic. Most countries failed to achieve immunization rates high enough to avoid resurgence of the virus. Public health strategies for autumn and winter 2021 have ranged from countries aiming at low incidence by re-introducing NPIs to accepting high incidence levels. However, such high incidence strategies almost certainly lead to the very consequences that they seek to avoid: restrictions that harm people and economies. At high incidence, the important pandemic containment measure 'test-trace-isolate-support' becomes inefficient. At that point, the spread of SARS-CoV-2 and its numerous harmful consequences can likely only be controlled through restrictions. We argue that all European countries need to pursue a low incidence strategy in a coordinated manner. Such an endeavour can only be successful if it is built on open communication and trust.