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Reputation and reciprocity : review
Chengyi Xia, Juan Wang, Matjaž Perc, Zhen Wang, 2023, review article

Abstract: Reputation and reciprocity are key mechanisms for cooperation in human societies, often going hand in hand to favor prosocial behavior over selfish actions. Here we review recent researches at the interface of physics and evolutionary game theory that explored these two mechanisms. We focus on image scoring as the bearer of reputation, as well as on various types of reciprocity, including direct, indirect, and network reciprocity. We review different definitions of reputation and reciprocity dynamics, and we show how these affect the evolution of cooperation in social dilemmas. We consider first-order, second-order, as well as higherorder models in well-mixed and structured populations, and we review experimental works that support and inform the results of mathematical modeling and simulations. We also provide a synthesis of the reviewed researches along with an outlook in terms of six directions that seem particularly promising to explore in the future.
Keywords: pattern formation, Monte Carlo method, complex network, evolutionary game theory, cooperation, social physics
Published in DKUM: 20.06.2024; Views: 28; Downloads: 0
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A game theoretical model for the stimulation of public cooperation in environmental collaborative governance
Yinhai Fang, Matjaž Perc, Hui Zhang, 2022, original scientific article

Abstract: Digital technologies provide a convenient way for the public to participate in environmental governance. Therefore, by means of a two-stage evolutionary model, a new mechanism for promoting public cooperation is proposed to accomplish environmental collaborative governance. Interactive effects of government-enterprise environmental governance are firstly explored, which is the external atmosphere for public behaviour. Second, the evolutionary dynamics of public behaviour is analysed to reveal the internal mechanism of the emergence of public cooperation in environmental collaborative governance projects. Simulations reveal that the interaction of resource elements between government and enterprise is an important basis for environmental governance performance, and that governments can improve this as well as public cooperation by increasing the marginal governance propensity. Similarly, an increase in the government's fixed expenditure item of environmental governance can also significantly improve government-enterprise performance and public cooperation. And finally, the effect of government's marginal incentive propensity on public environmental governance is moderated by enterprises' marginal environmental governance propensity, so that simply increasing the government's marginal incentive propensity cannot improve the evolutionary stable state of public behaviour under the scenario where enterprises’ marginal environmental governance propensity is low.
Keywords: game theory, human behaviour, cooperation, mathematical model, common goods
Published in DKUM: 28.05.2024; Views: 144; Downloads: 0

Axioms of decision criteria for 3D matrix games and their applications
Murat Özkaya, Burhaneddin İzgi, Matjaž Perc, 2022, original scientific article

Keywords: game theory, decision criteria, matrix game, common goods
Published in DKUM: 27.05.2024; Views: 137; Downloads: 0

Extended matrix norm method : applications to bimatrix games and convergence results
Burhaneddin İzgi, Murat Özkaya, Nazım Kemal Üre, Matjaž Perc, 2023, original scientific article

Abstract: In this paper, we extend and apply the Matrix Norm (MN) approach to the nonzero-sum bimatrix games. We present preliminary results regarding the convergence of the MN approaches. We provide a notation for expressing nonzero-sum bimatrix games in terms of two matrix games using the idea of separation of a bimatrix game into two different matrix games. Next, we prove theorems regarding boundaries of the game value depending on only norms of the payoff matrix for each player of the nonzero-sum bimatrix game. In addition to these, we refine the boundaries of the game value for the zero/nonzero sum matrix games. Therefore, we succeed to find an improved interval for the game value, which is a crucial improvement for both nonzero and zero-sum matrix games. As a consequence, we can solve a nonzero-sum bimatrix game for each player approximately without solving any equations. Moreover, we modify the inequalities for the extrema of the strategy set for the nonzero-sum bimatrix games. Furthermore, we adapt the min-max theorem of the MN approach for the nonzero-sum bimatrix games. Finally, we consider various bimatrix game examples from the literature, including the famous battle of sexes, to demonstrate the consistency of our approaches. We also show that the repeated applications of Extended Matrix Norm (EMN) methods work well to obtain a better-estimated game value in view of the obtained convergence results.
Keywords: game theory, nonzero sum game, bimatrix game, matrix norms, battle of sexes, convergence
Published in DKUM: 15.04.2024; Views: 234; Downloads: 235
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Sustainability in tourism determined by an asymmetric game with mobility
Manuel Chica, Juan M. Hernández, Matjaž Perc, 2022, original scientific article

Abstract: Many countries worldwide rely on tourism for their economic well-being and development. But with issues such as over-tourism and environmental degradation looming large, there is a pressing need to determine a way forward in a sustainable and mutually rewarding manner. With this motivation, we here propose an asymmetric evolutionary game with mobility where local stakeholders and tourists can either cooperate or defect in a spatially structured setting. Our study reflects that sustainable tourism is primarily determined by an optimal trade-off between economic benefits of the stakeholders and their costs related to the application of sustainability policies. In contrast, the specific benefits and costs of the tourists are comparatively less relevant. The reader can also observe that allowing for greater tourist mobility decreases cooperation and leads to faster polarization among local stakeholders. In agreement with observations worldwide, we identify decreasing population densities in tourist areas in terms of both, stakeholders and tourists, to be a key aid to greater cooperation and overall sustainability of tourism. These results are rooted in spatial formations and complex alliances that manifest spontaneously through the evolutionary dynamics in a structured population.
Keywords: asymmetric game, spatial structure, migration, evolutionary game theory, sustainable tourism, over-tourism
Published in DKUM: 24.08.2023; Views: 509; Downloads: 21
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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: 387; Downloads: 38
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Technological valley of death as an emergent evolutionary phenomenon
Petra Fic, 2019, master's thesis

Abstract: Perceptual researchers often argue that natural selection supports veridical perceptions, respectively those that accurately reflect the environment. They also claim that beings whose perceptions are truer are also more fit. This assumption was tested using standard tools of evolutionary game theory in a simple environment. The result was that more veridical perceptions are not necessarily more successful. In the majority of the parameter space, veridical perceptions are extinct in competition with simplified perceptions, based on adaptive behavior in a given environment. In the thesis, we build upon mentioned territorial games introduced by Mark, Marion, and Hoffman in 2010, and extend four of their territory perception and selection strategies with two novel ones that together constitute a model of technological readiness valley of death. Whenever utility of a resource is not monotonous in the amount of that resource, the technological valley of death emerges. While the development of the science behind these models is in its infancy, modeling and understanding the phenomenon may shed light on progress and related phenomena in society.
Keywords: evolution, perception, utility, Monte Carlo simulation, game theory
Published in DKUM: 22.11.2019; Views: 1704; Downloads: 174
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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: 1760; Downloads: 392
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Evolution of cooperation on scale-free networks subject to error and attack
Matjaž 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: 1521; Downloads: 363
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Emergence of multilevel selection in the prisoner's dilemma game on coevolving random networks
Attila 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: 1639; Downloads: 411
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