Inequality leads to the evolution of intolerance in reputation-based populations.

This work studies the impact of economic inequality on the evolution of intolerance through a reputation-based model of indirect reciprocity. Results show that economic inequality is a powerful enhancer of intolerance, inducing the escalation of out-group discrimination even without the presence of new intolerant mutants. It also generates behavior modifications within tolerant disfavored minorities: their members either relax punishments against the uncooperative or prioritize helping the wealthy, even suffering discrimination in return. On the other hand, the redistribution of wealth is proven as a viable solution to avoid the spread of intolerance as long as it increases equality and is implemented before intolerance permeates part of the population.

Signalling boosts the evolution of cooperation in repeated group interactions.

Many biological and social systems show significant levels of collective action. Several cooperation mechanisms have been proposed, yet they have been mostly studied independently. Among these, direct reciprocity supports cooperation on the basis of repeated interactions among individuals. Signals and quorum dynamics may also drive cooperation. Here, we resort to an evolutionary game-theoretical model to jointly analyse these two mechanisms and study the conditions in which evolution selects for direct reciprocity, signalling, or their combination. We show that signalling alone leads to higher levels of cooperation than when combined with reciprocity, while offering additional robustness against errors. Specifically, successful strategies in the realm of direct reciprocity are often not selected in the presence of signalling, and memory of past interactions is only exploited opportunistically in the case of earlier coordination failure. Differently, signalling always evolves, even when costly. In the light of these results, it may be easier to understand why direct reciprocity has been observed only in a limited number of cases among non-humans, whereas signalling is widespread at all levels of complexity.

Evolutionary dynamics of organised crime and terrorist networks.

Crime is pervasive into modern societies, although with different levels of diffusion across regions. Its dynamics are dependent on various socio-economic factors that make the overall picture particularly complex. While several theories have been proposed to account for the establishment of criminal behaviour, from a modelling perspective organised crime and terrorist networks received much less attention. In particular, the dynamics of recruitment into such organisations deserve specific considerations, as recruitment is the mechanism that makes crime and terror proliferate. We propose a framework able to model such processes in both organised crime and terrorist networks from an evolutionary game theoretical perspective. By means of a stylised model, we are able to study a variety of different circumstances and factors influencing the growth or decline of criminal organisations and terrorist networks, and observe the convoluted interplay between agents that decide to get associated to illicit groups, criminals that prefer to act on their own, and the rest of the civil society.

Individual perception dynamics in drunk games.

We study the effects of individual perceptions of payoffs in two-player games. In particular we consider the setting in which individuals' perceptions of the game are influenced by their previous experiences and outcomes. Accordingly, we introduce a framework based on evolutionary games where individuals have the capacity to perceive their interactions in different ways. Starting from the narrative of social behaviors in a pub as an illustration, we first study the combination of the Prisoner's Dilemma and Harmony Game as two alternative perceptions of the same situation. Considering a selection of game pairs, our results show that the interplay between perception dynamics and game payoffs gives rise to nonlinear phenomena unexpected in each of the games separately, such as catastrophic phase transitions in the cooperation basin of attraction, Hopf bifurcations and cycles of cooperation and defection. Combining analytical techniques with multiagent simulations, we also show how introducing individual perceptions can cause nontrivial dynamical behaviors to emerge, which cannot be obtained by analyzing the system at a macroscopic level. Specifically, initial perception heterogeneities at the microscopic level can yield a polarization effect that is unpredictable at the macroscopic level. This framework opens the door to the exploration of new ways of understanding the link between the emergence of cooperation and individual preferences and perceptions, with potential applications beyond social interactions.

When agreement-accepting free-riders are a necessary evil for the evolution of cooperation.

Agreements and commitments have provided a novel mechanism to promote cooperation in social dilemmas in both one-shot and repeated games. Individuals requesting others to commit to cooperate (proposers) incur a cost, while their co-players are not necessarily required to pay any, allowing them to free-ride on the proposal investment cost (acceptors). Although there is a clear complementarity in these behaviours, no dynamic evidence is currently available that proves that they coexist in different forms of commitment creation. Using a stochastic evolutionary model allowing for mixed population states, we identify non-trivial roles of acceptors as well as the importance of intention recognition in commitments. In the one-shot prisoner's dilemma, alliances between proposers and acceptors are necessary to isolate defectors when proposers do not know the acceptance intentions of the others. However, when the intentions are clear beforehand, the proposers can emerge by themselves. In repeated games with noise, the incapacity of proposers and acceptors to set up alliances makes the emergence of the first harder whenever the latter are present. As a result, acceptors will exploit proposers and take over the population when an apology-forgiveness mechanism with too low apology cost is introduced, and hence reduce the overall cooperation level.

Memory-n strategies of direct reciprocity.

Humans routinely use conditionally cooperative strategies when interacting in repeated social dilemmas. They are more likely to cooperate if others cooperated before, and are ready to retaliate if others defected. To capture the emergence of reciprocity, most previous models consider subjects who can only choose from a restricted set of representative strategies, or who react to the outcome of the very last round only. As players memorize more rounds, the dimension of the strategy space increases exponentially. This increasing computational complexity renders simulations for individuals with higher cognitive abilities infeasible, especially if multiplayer interactions are taken into account. Here, we take an axiomatic approach instead. We propose several properties that a robust cooperative strategy for a repeated multiplayer dilemma should have. These properties naturally lead to a unique class of cooperative strategies, which contains the classical Win-Stay Lose-Shift rule as a special case. A comprehensive numerical analysis for the prisoner's dilemma and for the public goods game suggests that strategies of this class readily evolve across various memory-n spaces. Our results reveal that successful strategies depend not only on how cooperative others were in the past but also on the respective context of cooperation.

Apology and forgiveness evolve to resolve failures in cooperative agreements.

Making agreements on how to behave has been shown to be an evolutionarily viable strategy in one-shot social dilemmas. However, in many situations agreements aim to establish long-term mutually beneficial interactions. Our analytical and numerical results reveal for the first time under which conditions revenge, apology and forgiveness can evolve and deal with mistakes within ongoing agreements in the context of the Iterated Prisoners Dilemma. We show that, when the agreement fails, participants prefer to take revenge by defecting in the subsisting encounters. Incorporating costly apology and forgiveness reveals that, even when mistakes are frequent, there exists a sincerity threshold for which mistakes will not lead to the destruction of the agreement, inducing even higher levels of cooperation. In short, even when to err is human, revenge, apology and forgiveness are evolutionarily viable strategies which play an important role in inducing cooperation in repeated dilemmas.

Spreading of intolerance under economic stress: results from a reputation-based model.

When a population is engaged in successive prisoner's dilemmas, indirect reciprocity through reputation fosters cooperation through the emergence of moral and action rules. A simplified model has recently been proposed where individuals choose between helping others or not and are judged good or bad for it by the rest of the population. The reputation so acquired will condition future actions. In this model, eight strategies (referred to as "leading eight") enforce a high level of cooperation, generate high payoffs, and are therefore resistant to invasions by other strategies. Here we show that, by assigning each individual one of two labels that peers can distinguish (e.g., political ideas, religion, and skin color) and allowing moral and action rules to depend on the label, intolerant behaviors can emerge within minorities under sufficient economic stress. We analyze the sets of conditions where this can happen and also discuss the circumstances under which tolerance can be restored. Our results agree with empirical observations that correlate intolerance and economic stress and predict a correlation between the degree of tolerance of a population and its composition and ethical stance.

Evolutionary stability and resistance to cheating in an indirect reciprocity model based on reputation.

Indirect reciprocity is one of the main mechanisms to explain the emergence and sustainment of altruism in societies. The standard approach to indirect reciprocity is reputation models. These are games in which players base their decisions on their opponent's reputation gained in past interactions with other players (moral assessment). The combination of actions and moral assessment leads to a large diversity of strategies; thus determining the stability of any of them against invasions by all the others is a difficult task. We use a variant of a previously introduced reputation-based model that let us systematically analyze all these invasions and determine which ones are successful. Accordingly, we are able to identify the third-order strategies (those which, apart from the action, judge considering both the reputation of the donor and that of the recipient) that are evolutionarily stable. Our results reveal that if a strategy resists the invasion of any other one sharing its same moral assessment, it can resist the invasion of any other strategy. However, if actions are not always witnessed, cheaters (i.e., individuals with a probability of defecting regardless of the opponent's reputation) have a chance to defeat the stable strategies for some choices of the probabilities of cheating and of being witnessed. Remarkably, by analyzing this issue with adaptive dynamics we find that whether an honest population resists the invasion of cheaters is determined by a Hamilton-like rule, with the probability that the cheat is discovered playing the role of the relatedness parameter.

Generosity pays in the presence of direct reciprocity: a comprehensive study of 2 × 2 repeated games.

By applying a technique previously developed to study ecosystem assembly [Capitán et al., Phys. Rev. Lett. 103, 168101 (2009)] we study the evolutionary stable strategies of iterated 2 × 2 games. We focus on memory-one strategies, whose probability to play a given action depends on the actions of both players in the previous time step. We find the asymptotically stable populations resulting from all possible invasions of any known stable population. The results of this invasion process are interpreted as transitions between different populations that occur with a certain probability. Thus the whole process can be described as a Markov chain whose states are the different stable populations. With this approach we are able to study the whole space of symmetric 2 × 2 games, characterizing the most probable results of evolution for the different classes of games. Our analysis includes quasi-stationary mixed equilibria that are relevant as very long-lived metastable states and is compared to the predictions of a fixation probability analysis. We confirm earlier results on the success of the Pavlov strategy in a wide range of parameters for the iterated Prisoner's Dilemma, but find that as the temptation to defect grows there are many other possible successful strategies. Other regions of the diagram reflect the equilibria structure of the underlying one-shot game, albeit often some non-expected strategies arise as well. We thus provide a thorough analysis of iterated 2 × 2 games from which we are able to extract some general conclusions. Our most relevant finding is that a great deal of the payoff parameter range can still be understood by focusing on win-stay, lose-shift strategies, and that very ambitious ones, aspiring to obtaining always a high payoff, are never evolutionary stable.