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1.
Eco-evolutionary dynamics of multigames with mutations
Sourav Roy, Sayantan Nag Chowdhury, Prakash Chandra Mali, Matjaž Perc, Dibakar Ghosh, 2022, original scientific article

Abstract: Most environments favor defection over cooperation due to natural selection. Nonetheless, the emergence of cooperation is omnipresent in many biological, social, and economic systems, quite contrary to the well-celebrated Darwinian theory of evolution. Much research has been devoted to better understanding how and why cooperation persists among selfinterested individuals despite their competition for limited resources. Here we go beyond a single social dilemma since individuals usually encounter various social challenges. In particular, we propose and study a mathematical model incorporating both the prisoner’s dilemma and the snowdrift game. We further extend this model by considering ecological signatures like mutation and selfless one-sided contribution of altruist free space. The nonlinear evolutionary dynamics that results from these upgrades offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection. With the help of analytical and numerical calculations, our theoretical model sheds light on the mechanisms that maintain biodiversity, and it helps to explain the evolution of social order in human societies.
Keywords: public goods, cooperation, mutation, social physics, evolutionary dynamics
Published in DKUM: 15.07.2024; Views: 137; Downloads: 9
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2.
The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players
Atefeh Ahmadi, Sourav Roy, Mahtab Mehrabbeik, Dibakar Ghosh, Sajad Jafari, Matjaž Perc, 2023, original scientific article

Abstract: One of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the convergence to its Nash equilibrium, but the dynamics of real-world markets are not always steady and can result in unpredictable market changes that exhibit chaotic behaviors. On the other hand, to approach reality more, the two firms in the market can be considered heterogeneous. The leader firm is bounded rationale, and the follower firm is adaptable. Modifying the cost function that affects the firms' profit by adding the marginal cost term is another step toward reality. We propose a Stackelberg model with heterogeneous players and marginal costs, which exhibits chaotic behavior. This model's equilibrium points, including the Nash equilibrium, are calculated by the backward induction method, and their stability analyses are obtained. The influence of changing each model parameter on the consequent dynamics is investigated through one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. Eventually, using a combination of state feedback and parameter adjustment methods, the chaotic solutions of the model are successfully tamed, and the model converges to its Nash equilibrium.
Keywords: nonlinear dynamics, game theory, stability analysis, public goods
Published in DKUM: 02.08.2023; Views: 459; Downloads: 44
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3.
Different approaches to cross border mobility of patients in the European Union in Czechia, Slovakia and Poland
Filip Křepelka, 2016, original scientific article

Abstract: Poland and Slovakia are neighbour countries with similar history and socioeconomic conditions. They share heritage of socialized healthcare. Nevertheless, they adopted different policies towards promotion of patients´ mobility in the European Union. Accession to coordination of social security establishing assistance for tourists was smooth. Providers offer quality care for good prices. Foreign patients come to all three countries. Right for reimbursement of treatment intentionally sought across borders was created by the Court of Justice already before their accession. Nevertheless, they already decided on the Patients´ directive. Czechia supported it, Slovakia abstained and Poland refused. Numerous Poles seek treatment abroad and ask for its reimbursement, while implementing legislation barely complies and authorities are tight-fisted. Few Slovaks do it in accordance with rules adopted with cautiousness. Czechs ignore this opportunity despite official benevolence. Quality of healthcare, various price-setting and peculiarities of public financing explain this difference.
Keywords: European Union, free movement of services and goods, medical tourism, public financing of healthcare, patients' rights
Published in DKUM: 09.10.2018; Views: 1201; Downloads: 66
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4.
Determinants of public cooperation in multiplex networks
Federico Battiston, Matjaž Perc, Vito Latora, 2017, original scientific article

Abstract: Synergies between evolutionary game theory and statistical physics have significantly improved our understanding of public cooperation in structured populations. Multiplex networks, in particular, provide the theoretical framework within network science that allows us to mathematically describe the rich structure of interactions characterizing human societies. While research has shown that multiplex networks may enhance the resilience of cooperation, the interplay between the overlap in the structure of the layers and the control parameters of the corresponding games has not yet been investigated. With this aim, we consider here the public goods game on a multiplex network, and we unveil the role of the number of layers and the overlap of links, as well as the impact of different synergy factors in different layers, on the onset of cooperation. We show that enhanced public cooperation emerges only when a significant edge overlap is combined with at least one layer being able to sustain some cooperation by means of a sufficiently high synergy factor. In the absence of either of these conditions, the evolution of cooperation in multiplex networks is determined by the bounds of traditional network reciprocity with no enhanced resilience. These results caution against overly optimistic predictions that the presence of multiple social domains may in itself promote cooperation, and they help us better understand the complexity behind prosocial behavior in layered social systems.
Keywords: cooperation, public goods, networks, physics of social systems
Published in DKUM: 04.12.2017; Views: 1271; Downloads: 398
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5.
Correlation of positive and negative reciprocity fails to confer an evolutionary advantage: phase transitions to elementary strategies
Attila Szolnoki, Matjaž Perc, 2013, original scientific article

Abstract: Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavioris therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionarily advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding, and punishment, a fourth strategy that combines the latter two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet, despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments.
Keywords: public goods, punishment, reward, evolutionary games, collective phenomena, phase transitions, physics of social systems
Published in DKUM: 03.08.2017; Views: 1276; Downloads: 368
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6.
Self-organization of punishment in structured populations
Matjaž Perc, Attila Szolnoki, 2012, original scientific article

Abstract: Cooperation is crucial for the remarkable evolutionary success of the human species. Not surprisingly, some individuals are willing to bear additional costs in order to punish defectors. Current models assume that, once set, the fine and cost of punishment do not change over time. Here we show that relaxing this assumption by allowing players to adapt their sanctioning efforts in dependence on the success of cooperation can explain both the spontaneous emergence of punishment and its ability to deter defectors and those unwilling to punish them with globally negligible investments. By means of phase diagrams and the analysis of emerging spatial patterns, we demonstrate that adaptive punishment promotes public cooperation through the invigoration of spatial reciprocity, the prevention of the emergence of cyclic dominance, or the provision of competitive advantages to those that sanction antisocial behavior. The results presented indicate that the process of self-organization significantly elevates the effectiveness of punishment, and they reveal new mechanisms by means of which this fascinating and widespread social behavior could have evolved.
Keywords: cooperation, public goods, punishment, phase transitions, physics of social systems
Published in DKUM: 03.07.2017; Views: 1203; Downloads: 433
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7.
Punish, but not too hard: how costly punishment spreads in the spatial public goods game
Dirk Helbing, Attila Szolnoki, Matjaž Perc, György Szabó, 2010, original scientific article

Abstract: We study the evolution of cooperation in spatial public goods games where, besides the classical strategies of cooperation (C) and defection (D), we consider punishing cooperators (PC) or punishing defectors (PD) as an additional strategy. Using a minimalist modeling approach, our goal is to separately clarify and identify the consequences of the two punishing strategies. Since punishment is costly, punishing strategies lose the evolutionary competition in case of well-mixed interactions. When spatial interactions are taken into account, however, the outcome can be strikingly different, and cooperation may spread. The underlying mechanism depends on the character of the punishment strategy. In the case of cooperating punishers,increasing the fine results in a rising cooperation level. In contrast, in the presence of the PD strategy, the phase diagram exhibits a reentrant transition as the fine is increased. Accordingly, the level of cooperation shows a non-monotonous dependence on the fine. Remarkably, punishing strategies can spread in both cases, but based on largely different mechanisms, which depend on the cooperativeness (or not) of punishers.
Keywords: evolutionary game theory, public goods, spatial games, punishment, social systems, moral
Published in DKUM: 03.07.2017; Views: 1855; Downloads: 405
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8.
Probabilistic sharing solves the problem of costly punishment
Xiaojie Chen, Attila Szolnoki, Matjaž Perc, 2014, original scientific article

Abstract: Cooperators that refuse to participate in sanctioning defectors create the secondorder free-rider problem. Such cooperators will not be punished because they contribute to the public good, but they also eschew the costs associated with punishing defectors. Altruistic punishers - those that cooperate and punish - are at a disadvantage, and it is puzzling how such behaviour has evolved. We show that sharing the responsibility to sanction defectors rather than relying on certain individuals to do so permanently can solve the problem of costly punishment. Inspired by the fact that humans have strong but also emotional tendencies for fair play, we consider probabilistic sanctioning as the simplest way of distributing the duty. In well-mixed populations the public goods game is transformed into a coordination game with full cooperation and defection as the two stable equilibria, while in structured populations pattern formation supports additional counterintuitive solutions that are reminiscent of Parrondoʼs paradox.
Keywords: social dynamics, networks, punishment, public goods, econophysics
Published in DKUM: 03.07.2017; Views: 1274; Downloads: 424
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9.
Information sharing promotes prosocial behaviour
Attila 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: 446
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10.
Evolutionary advantages of adaptive rewarding
Attila Szolnoki, Matjaž Perc, 2012, original scientific article

Abstract: Our well-being depends on both our personal success and the success of our society. The realization of this fact makes cooperation an essential trait. Experiments have shown that rewards can elevate our readiness to cooperate, but since giving a reward inevitably entails paying a cost for it, the emergence and stability of such behavior remains elusive. Here we show that allowing for the act of rewarding to self-organize in dependence on the success of cooperation creates several evolutionary advantages that instill new ways through which collaborative efforts are promoted. Ranging from indirect territorial battle to the spontaneous emergence and destruction of coexistence, phase diagrams and the underlying spatial patterns reveal fascinatingly rich social dynamics that explain why this costly behavior has evolved and persevered. Comparisons with adaptive punishment, however, uncover an Achilles heel of adaptive rewarding, coming from over-aggression, which in turn hinders optimal utilization of network reciprocity. This may explain why, despite its success, rewarding is not as firmly embedded into our societal organization as punishment.
Keywords: cooperation, public goods, reward, punishment, phase transitions, physics of social systems
Published in DKUM: 30.06.2017; Views: 1643; Downloads: 421
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