1. Seasonal payoff variations and the evolution of cooperation in social dilemmasAttila Szolnoki, Matjaž Perc, 2019, original scientific article Abstract: Varying environmental conditions affect relations between interacting individuals in social dilemmas, thus affecting also the evolution of cooperation. Oftentimes these environmental variations are seasonal and can therefore be mathematically described as periodic changes. Accordingly, we here study how periodic shifts between different manifestations of social dilemmas affect cooperation. We observe a non-trivial interplay between the inherent spatiotemporal dynamics that characterizes the spreading of cooperation in a particular social dilemma type and the frequency of payoff changes. In particular, we show that periodic changes between two available games with global ordering best be fast, while periodic changes between global and local ordering games best be slow for cooperation to thrive. We also show that the frequency of periodic changes between two local ordering social dilemmas is irrelevant, because then the process is fast and simply the average cooperation level of the two is returned. The structure of the interaction network plays an important role too in that lattices promote local ordering, whilst random graphs hinder the formation of compact cooperative clusters. Conversely, for local ordering the regular structure of the interaction network is only marginally relevant as role-separating checkerboard patterns do not rely on long-range order. Keywords: cooperation, social dilemma, social physics, phase transition, mixed games Published in DKUM: 26.02.2025; Views: 0; Downloads: 2
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2. Communicating sentiment and outlook reverses inaction against collective risksZhen Wang, Marko Jusup, Hao Guo, Lei Shi, Sunčana Geček, Madhur Anand, Matjaž Perc, Chris T. Bauch, Jürgen Kurths, Stefano Boccaletti, Hans-Joachim Schellnhuber, 2020, original scientific article Abstract: 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. This reveals that the mechanisms behind avoiding collective risks depend on an interaction between behavioral type, communication, and timing. Keywords: social dilemma, free riding, climate change, negotiation, group size, COVID-19 Published in DKUM: 07.01.2025; Views: 0; Downloads: 4
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3. Time delays shape the eco‑evolutionary dynamics of cooperationSourav Roy, Sayantan Nag Chowdhury, Srilena Kundu, Gourab Kumar Sar, Jeet Banerjee, Biswambhar Rakshit, Prakash Chandra Mali, Matjaž Perc, Dibakar Ghosh, 2023, original scientific article Abstract: We study the intricate interplay between ecological and evolutionary processes through the lens of the prisoner’s dilemma game. But while previous studies on cooperation amongst selfsh individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might afect the causes underlying prosocial behavior. Through analytical calculations and numerical simulations, we demonstrate that delays can lead to oscillations, and by incorporating also the ecological variable of altruistic free space and the evolutionary strategy of punishment, we explore how these factors impact population and community dynamics. Depending on the parameter values and the initial fraction of each strategy, the studied eco-evolutionary model can mimic a cyclic dominance system and even exhibit chaotic behavior, thereby highlighting the importance of complex dynamics for the efective management and conservation of ecological communities. Our research thus contributes to the broader understanding of group decision-making and the emergence of moral behavior in multidimensional social systems. Keywords: cooperation, time delay, evolutionary dynamics, social dilemma, social physics Published in DKUM: 04.04.2024; Views: 191; Downloads: 18
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4. Information sharing promotes prosocial behaviourAttila Szolnoki, Matjaž Perc, 2013, original scientific article Abstract: More often than not, bad decisions are bad regardless of where and when they are made. Information sharing might thus be utilized to mitigate them. Here we show that sharing information about strategy choice between players residing on two different networks reinforces the evolution of cooperation. In evolutionary games, the strategy reflects the action of each individual that warrants the highest utility in a competitive setting. We therefore assume that identical strategies on the two networks reinforce themselves by lessening their propensity to change. Besides network reciprocity working in favour of cooperation on each individual network, we observe the spontaneous emergence of correlated behaviour between the two networks, which further deters defection. If information is shared not just between individuals but also between groups, the positive effect is even stronger, and this despite the fact that information sharing is implemented without any assumptions with regard to content. Keywords: cooperation, information, social dilemma, public goods, interdependent networks, statistical physics of social systems Published in DKUM: 03.07.2017; Views: 1258; Downloads: 449
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5. Evolution of cooperation on scale-free networks subject to error and attackMatjaž Perc, 2009, original scientific article Abstract: We study the evolution of cooperation in the prisoner's dilemma and the snowdrift game on scale-free networks that are subjected to intentional and random removal of vertices. We show that, irrespective of the game type, cooperation on scale-free networks is extremely robust against random deletionof vertices, but declines quickly if vertices with the maximal degree are targeted. In particular, attack tolerance is lowest if the temptation to defect is largest, whereby a small fraction of removed vertices suffices to decimate cooperators. The decline of cooperation can be directly linked to the decrease of heterogeneity of scale-free networks that sets in due to the removal of high degree vertices. We conclude that the evolution of cooperation is characterized by similar attack and error tolerance as was previously reported for information readiness and spread of viruses on scale-free networks. Keywords: evolutionary game theory, social dilemma, spatial games, complex networks Published in DKUM: 30.06.2017; Views: 1622; Downloads: 382
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6. Emergence of multilevel selection in the prisoner's dilemma game on coevolving random networksAttila Szolnoki, Matjaž Perc, 2009, original scientific article Abstract: We study the evolution of cooperation in the prisoner's dilemma game, whereby a coevolutionary rule is introduced that molds the random topology of the interaction network in two ways. First, existing links are deleted whenever a player adopts a new strategy or its degree exceeds a threshold value; second, new links are added randomly after a given number of game iterations. These coevolutionary processes correspond to the generic formation of new links and deletion of existing links that, especially in human societies, appear frequently as a consequence of ongoing socialization, change of lifestyle or death. Due to the counteraction of deletions and additions of links the initial heterogeneity of the interaction network is qualitatively preserved, and thus cannot be held responsible for the observed promotion of cooperation. Indeed, the coevolutionary rule evokes the spontaneous emergence of a powerful multilevel selection mechanism, which despite the sustained random topology of the evolving network, maintains cooperation across the whole span of defection temptation values. Keywords: evolutionary game theory, prisoner's dilemma, spatial games, coevolution, social systems Published in DKUM: 30.06.2017; Views: 1738; Downloads: 423
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7. Stability of cooperation under image scoring in group interactionsHeinrich H. Nax, Matjaž Perc, Attila Szolnoki, Dirk Helbing, 2015, original scientific article Abstract: Image scoring sustains cooperation in the repeated two-player prisoner's dilemma through indirect reciprocity, even though defection is the uniquely dominant selfish behaviour in the one-shot game. Many real-world dilemma situations, however, firstly, take place in groups and, secondly, lack the necessary transparency to inform subjects reliably of others' individual past actions. Instead, there is revelation of information regarding groups, which allows for "group scoring" but not for image scoring. Here, we study how sensitive the positive results related to image scoring are to information based on group scoring. We combine analytic results and computer simulations to specify the conditions for the emergence of cooperation. We show that under pure group scoring, that is, under the complete absence of image-scoring information, cooperation is unsustainable. Away from this extreme case, however, the necessary degree of image scoring relative to group scoring depends on the population size and is generally very small. We thus conclude that the positive results based on image scoring apply to a much broader range of informational settings that are relevant in the real world than previously assumed. Keywords: public goods, group interactions, phase transition, social dilemma, physics of social systems Published in DKUM: 23.06.2017; Views: 1526; Downloads: 463
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8. Spreading of cooperative behaviour across interdependent groupsLuo-Luo Jiang, Matjaž Perc, 2013, original scientific article Abstract: Recent empirical research has shown that links between groups reinforce individuals within groups to adopt cooperative behaviour. Moreover, links between networks may induce cascading failures, competitive percolation, or contribute to efficient transportation. Here we show that there in fact exists an intermediate fraction of links between groups that is optimal for the evolution of cooperation in the prisoners dilemma game. We consider individual groups with regular, random, and scale-free topology, and study their different combinations to reveal that an intermediate interdependence optimally facilitates the spreading of cooperative behaviour between groups. Excessive between-group links simply unify the two groups and make them act as one, while too rare between-group links preclude a useful information flow between the two groups. Interestingly, we find that between-group links are more likely to connect two cooperators than in-group links, thus supporting the conclusion that they are of paramount importance. Keywords: social dilemma, cooperation, public goods, biased utility, interdependent networks, statistical physics of social systems Published in DKUM: 23.06.2017; Views: 1795; Downloads: 426
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9. Optimal interdependence between networks for the evolution of cooperationZhen Wang, Attila Szolnoki, Matjaž Perc, 2013, original scientific article Abstract: Recent research has identified interactions between networks as crucial for the outcome of evolutionary games taking place on them. While the consensus is that interdependence does promote cooperation by means of organizational complexity and enhanced reciprocity that is out of reach on isolated networks, we here address the question just how much interdependence there should be. Intuitively, one might assume the more the better. However, we show that in fact only an intermediate density of sufficiently strong interactions between networks warrants an optimal resolution of social dilemmas. This is due to an intricate interplay between the heterogeneity that causes an asymmetric strategy flow because of the additional links between the networks, and the independent formation of cooperative patterns on each individual network. Presented results are robust to variations of the strategy updating rule, the topology of interdependent networks, and the governing social dilemma, thus suggesting a high degree of universality. Keywords: social dilemma, cooperation, public goods, biased utility, interdependent networks, statistical physics of social systems Published in DKUM: 23.06.2017; Views: 1213; Downloads: 385
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10. Interdependent network reciprocity in evolutionary gamesZhen Wang, Attila Szolnoki, Matjaž Perc, 2013, original scientific article Abstract: Besides the structure of interactions within networks, also the interactions between networks are of the outmost importance. We therefore study the outcome of the public goods game on two interdependent networks that are connected by means of a utility function, which determines how payoffs on both networks jointly influence the success of players in each individual network. We show that an unbiased coupling allows the spontaneous emergence of interdependent network reciprocity, which is capable to maintain healthy levels of public cooperation even in extremely adverse conditions. The mechanism, however, requires simultaneous formation of correlated cooperator clusters on both networks. If this does not emerge or if the coordination process is disturbed, network reciprocity fails, resulting in the total collapse of cooperation. Network interdependence can thus be exploited effectively to promote cooperation past the limits imposed by isolated networks, but only if the coordination between the interdependent networks is not disturbed. Keywords: social dilemma, cooperation, public goods, biased utility, interdependent networks, statistical physics of social systems Published in DKUM: 23.06.2017; Views: 1288; Downloads: 397
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