1
|
Xiong X, Zeng Z, Feng M, Szolnoki A. Coevolution of relationship and interaction in cooperative dynamical multiplex networks. CHAOS (WOODBURY, N.Y.) 2024; 34:023118. [PMID: 38363961 DOI: 10.1063/5.0188168] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 01/15/2024] [Indexed: 02/18/2024]
Abstract
While actors in a population can interact with anyone else freely, social relations significantly influence our inclination toward particular individuals. The consequence of such interactions, however, may also form the intensity of our relations established earlier. These dynamical processes are captured via a coevolutionary model staged in multiplex networks with two distinct layers. In a so-called relationship layer, the weights of edges among players may change in time as a consequence of games played in the alternative interaction layer. As an reasonable assumption, bilateral cooperation confirms while mutual defection weakens these weight factors. Importantly, the fitness of a player, which basically determines the success of a strategy imitation, depends not only on the payoff collected from interactions, but also on the individual relationship index calculated from the mentioned weight factors of related edges. Within the framework of weak prisoner's dilemma situation, we explore the potential outcomes of the mentioned coevolutionary process where we assume different topologies for relationship layer. We find that higher average degree of the relationship graph is more beneficial to maintain cooperation in regular graphs, but the randomness of links could be a decisive factor in harsh situations. Surprisingly, a stronger coupling between relationship index and fitness discourage the evolution of cooperation by weakening the direct consequence of a strategy change. To complete our study, we also monitor how the distribution of relationship index vary and detect a strong relation between its polarization and the general cooperation level.
Collapse
Affiliation(s)
- Xiaojin Xiong
- The College of Artificial Intelligence, Southwest University, No.2 Tiansheng Road, Beibei, Chongqing 400715, China
| | - Ziyan Zeng
- The College of Artificial Intelligence, Southwest University, No.2 Tiansheng Road, Beibei, Chongqing 400715, China
| | - Minyu Feng
- The College of Artificial Intelligence, Southwest University, No.2 Tiansheng Road, Beibei, Chongqing 400715, China
| | - Attila Szolnoki
- Institute of Technical Physics and Materials Science, Centre for Energy Research, P.O. Box 49, H-1525 Budapest, Hungary
| |
Collapse
|
2
|
Jing Y, Han S, Feng M, Kurths J. Co-evolution of heterogeneous cognition in spatial snowdrift game with asymmetric cost. CHAOS (WOODBURY, N.Y.) 2024; 34:023109. [PMID: 38341764 DOI: 10.1063/5.0192619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Accepted: 01/11/2024] [Indexed: 02/13/2024]
Abstract
The emergence of the evolutionary game on complex networks provides a fresh framework for studying cooperation behavior between complex populations. Numerous recent progress has been achieved in studying asymmetric games. However, there is still a substantial need to address how to flexibly express the individual asymmetric nature. In this paper, we employ mutual cognition among individuals to elucidate the asymmetry inherent in their interactions. Cognition arises from individuals' subjective assessments and significantly influences their decision-making processes. In social networks, mutual cognition among individuals is a persistent phenomenon and frequently displays heterogeneity as the influence of their interactions. This unequal cognitive dynamic will, in turn, influence the interactions, culminating in asymmetric outcomes. To better illustrate the inter-individual cognition in asymmetric snowdrift games, the concept of favor value is introduced here. On this basis, the evolution of cognition and its relationship with asymmetry degree are defined. In our simulation, we investigate how game cost and the intensity of individual cognitive changes impact the cooperation frequency. Furthermore, the temporal evolution of individual cognition and its variation under different parameters was also examined. The simulation results reveal that the emergence of heterogeneous cognition effectively addresses social dilemmas, with asymmetric interactions among individuals enhancing the propensity for cooperative choices. It is noteworthy that distinctions exist in the rules governing cooperation and cognitive evolution between regular networks and Watts-Strogatz small-world networks. In light of this, we deduce the relationship between cognition evolution and cooperative behavior in co-evolution and explore potential factors influencing cooperation within the system.
Collapse
Affiliation(s)
- Yuxuan Jing
- College of Artificial Intelligence, Southwest University, Chongqing 400715, China
| | - Songlin Han
- College of Han Hong, Southwest University, Chongqing 400715, China
| | - Minyu Feng
- College of Artificial Intelligence, Southwest University, Chongqing 400715, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, 14437 Potsdam, Germany
- Institute of Physics, Humboldt University, Berlin 12489, Germany
| |
Collapse
|
3
|
Xie Y, Han W, Qi J, Zhao Z. Cooperation with dynamic asymmetric evaluation in complex networks from a risk perspective. CHAOS (WOODBURY, N.Y.) 2024; 34:013115. [PMID: 38198681 DOI: 10.1063/5.0177804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2023] [Accepted: 11/15/2023] [Indexed: 01/12/2024]
Abstract
The choice of strategy exposes individuals to the risk of betrayal. This induces individuals' irrational tendencies in strategy selection, which further influences the emergence of cooperative behavior. However, the underlying mechanisms connecting risk perception and the emergence of cooperation are still not fully understood. To address this, the classic evolutionary game model on complex networks is extended. We depict the interaction between strategy imitation and payoff evaluation from two perspectives: dynamic adjustment and irrational assessment. Specifically, the probability distortion involved in the dynamic selection of imitative reference points, as well as the asymmetric psychological utility associated with reference point dependence, is emphasized. Monte Carlo simulations demonstrate that individual irrational cognition induced by the risk of strategy selection can promote the emergence of cooperative behavior. Among them, the risk sensitivity within psychological utility has the most significant moderating effect. Moreover, the promoting effect of strong heterogeneity and high clustering in the network topology on cooperation under risk scenarios has been clarified. Additionally, the influence of initial states on the emergence of cooperation follows a step-like pattern. This research offers valuable insights for further exploring the cooperation mechanisms among irrational agents, even in scenarios involving the regulation of group cooperation behavior in risky situations.
Collapse
Affiliation(s)
- Yunya Xie
- School of Management Science and Engineering, Tianjin University of Finance and Economics, Tianjin 300222, China
| | - Wei Han
- Business School, Southwest University of Political Science and Law, Chongqing 401120, China
| | - Jiaxin Qi
- School of Science and Technology, Tianjin University of Finance and Economics, Tianjin 300222, China
| | - Ziwen Zhao
- School of Management Science and Engineering, Tianjin University of Finance and Economics, Tianjin 300222, China
| |
Collapse
|
4
|
Lu S, Zhu G, Zhang L. The promoting effect of adaptive persistence aspiration on the cooperation based on the consideration of payoff and environment in prisoner's dilemma game. Biosystems 2023; 226:104868. [PMID: 36841505 DOI: 10.1016/j.biosystems.2023.104868] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2023] [Revised: 02/19/2023] [Accepted: 02/20/2023] [Indexed: 02/26/2023]
Abstract
This work explores whether holding the last aspiration for a period of time can promote cooperation. Specifically, an evolutionary spatial prisoner's dilemma game mode is proposed, in which the players adjust strategies and aspirations by considering the payoff and environment. Therefore, the core is to allow players to hold the current aspiration for a period of time. Through numerical calculation, this study finds that the existence of an appropriate duration of aspiration can promote cooperation when b is less than a certain value. Moreover, the cooperation is gradually enhanced with the increase of T-max (maximum aspiration duration) when b is greater than it, but the enhancing effect is limited. It is also found that an appropriate value α (sensitivity to environmental change) can promote cooperation at different b intervals. Besides, this system indicates good robustness. Overall, this study provides a new perspective on exploring cooperative evolution based on aspiration.
Collapse
Affiliation(s)
- Shounan Lu
- School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China.
| | - Ge Zhu
- School of Information Management, Beijing Information Science and Technology University, Beijing, 100192, China; Owen Graduate School of Management, Vanderbilt University, Nashville, 37203, USA
| | - Lianzhong Zhang
- School of Physics, Nankai University, Tianjin, 300071, China.
| |
Collapse
|
5
|
Fan L, Song Z, Wang L, Liu Y, Wang Z. Incorporating social payoff into reinforcement learning promotes cooperation. CHAOS (WOODBURY, N.Y.) 2022; 32:123140. [PMID: 36587319 DOI: 10.1063/5.0093996] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 12/01/2022] [Indexed: 06/17/2023]
Abstract
Reinforcement learning has been demonstrated to be an effective approach to investigate the dynamic of strategy updating and the learning process of agents in game theory. Most studies have shown that Q-learning failed to resolve the problem of cooperation in well-mixed populations or homogeneous networks. To this aim, we investigate the self-regarding Q-learning's effect on cooperation in spatial prisoner's dilemma games by incorporating the social payoff. Here, we redefine the reward term of self-regarding Q-learning by involving the social payoff; that is, the reward is defined as a monotonic function of the individual payoff and the social payoff represented by its neighbors' payoff. Numerical simulations reveal that such a framework can facilitate cooperation remarkably because the social payoff ensures agents learn to cooperate toward socially optimal outcomes. Moreover, we find that self-regarding Q-learning is an innovative rule that ensures cooperators coexist with defectors even at high temptations to defection. The investigation of the emergence and stability of the sublattice-ordered structure shows that such a mechanism tends to generate a checkerboard pattern to increase agents' payoff. Finally, the effects of Q-learning parameters are also analyzed, and the robustness of this mechanism is verified on different networks.
Collapse
Affiliation(s)
- Litong Fan
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Zhao Song
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Lu Wang
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Yang Liu
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Zhen Wang
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| |
Collapse
|
6
|
Zhang M, Zhang X, Qu C, Wang G, Lu X. The combination of social reward and punishment is conducive to the cooperation and heterogeneity of social relations. CHAOS (WOODBURY, N.Y.) 2022; 32:103104. [PMID: 36319289 DOI: 10.1063/5.0102483] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2022] [Accepted: 09/06/2022] [Indexed: 06/16/2023]
Abstract
Individual behaviors and social relations influence each other. However, understanding the underlying mechanism remains challenging. From social norms controlling human behavior to individual management of interpersonal relationships, rewards and punishments are some of the most commonly used measures. Through simulating the weak prisoner's dilemma in finite populations, we find that neither a simple reward measure nor a pure punishment mechanism can extensively promote cooperation. Instead, a combination of appropriate punishment and reward mechanisms can promote cooperation's prosperity regardless of how large or small the temptation to defect is. In addition, the combination spontaneously produces inhomogeneities in social relations and individual influence, which support the continued existence of cooperative behavior. Finally, we further explain how cooperators establish a sustainable existence under the combination by investigating the social relations at different moments in a small system. These results demonstrate that dispensing rewards and punishments impartially in society is essential to social harmony.
Collapse
Affiliation(s)
- Ming Zhang
- School of Mathematics, Shandong University, Jinan 250100, People's Republic of China
| | - Xu Zhang
- Data Science Institute, Shandong University, Jinan 250100, People's Republic of China
| | - Cunquan Qu
- Data Science Institute, Shandong University, Jinan 250100, People's Republic of China
| | - Guanghui Wang
- School of Mathematics, Shandong University, Jinan 250100, People's Republic of China
| | - Xin Lu
- College of Systems Engineering, National University of Defense Technology, Changsha 410073, People's Republic of China
| |
Collapse
|
7
|
Zhang L, Zhang L, Huang C. Defectors in bad circumstances possessing higher reputation can promote cooperation. CHAOS (WOODBURY, N.Y.) 2022; 32:043114. [PMID: 35489841 DOI: 10.1063/5.0084901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Accepted: 03/22/2022] [Indexed: 06/14/2023]
Abstract
In nature and human society, social relationships and behavior patterns are usually unpredictable. In any interaction, individuals will constantly have to deal with prior uncertainty. The concept of "reputation" can provide some information to mitigate such uncertainty. In previous studies, researchers have considered that only cooperators are able to maintain a high reputation; no matter the circumstances of a defector, they are classified as a faithless individual. In reality, however, some individuals will be forced to defect to protect themselves against exploitation. Therefore, it makes sense that defectors in bad circumstances could also obtain higher reputations, and cooperators can maintain higher reputations in comfortable circumstances. In this work, the reputations of individuals are calculated using the fraction of their neighbors who have the same strategy. In this way, some defectors in a population may obtain higher reputations than some cooperators. We introduce this reputation rule using heterogeneous investments in public goods games. Our numerical simulation results indicate that this reputation rule and heterogeneous investments can better stimulate cooperation. Additionally, stronger investment heterogeneity can further increase the level of cooperation. To explain this phenomenon, dynamical evolution is observed in Monte Carlo simulations. We also investigated the effects of the noise intensity of the irrational population and the original proportion of cooperation in the population. The robustness of this cooperation model was also considered with respect to the network structure and total investment, and we found that the conclusions remained the same.
Collapse
Affiliation(s)
- Lan Zhang
- School of Information, Xi'an University of Finance and Economics, Xi'an 710100, China
| | - Liming Zhang
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Changwei Huang
- School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China
| |
Collapse
|
8
|
Tang Y, Kurths J, Lin W, Ott E, Kocarev L. Introduction to Focus Issue: When machine learning meets complex systems: Networks, chaos, and nonlinear dynamics. CHAOS (WOODBURY, N.Y.) 2020; 30:063151. [PMID: 32611112 DOI: 10.1063/5.0016505] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2020] [Accepted: 06/05/2020] [Indexed: 06/11/2023]
Affiliation(s)
- Yang Tang
- Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
| | - Wei Lin
- Center for Computational Systems Biology of ISTBI and Research Institute of Intelligent Complex Systems, Fudan University, Shanghai 200433, China
| | - Edward Ott
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Ljupco Kocarev
- Macedonian Academy of Sciences and Arts, 1000 Skopje, Macedonia
| |
Collapse
|