Article
Computer Science, Cybernetics
Xiaoyue Jin, Zhen Wang, Dengxiu Yu, Xuelong Li
Summary: In this article, a convergence analysis method for evolution dynamics in information loss networks is proposed to overcome the analytical difficulties caused by complex network relationships. A dynamic model of continuous action iterated dilemma (CAID) with continuous strategy is introduced to enrich the strategies of players and provide a more accurate representation of the evolution of cooperation. A new convergence analysis method based on the Lyapunov function is designed to avoid the complex calculations required by traditional models. The convergence of dynamic models in information loss networks is further analyzed using the Lyapunov function considering the presence of noise in information transfer.
IEEE TRANSACTIONS ON COMPUTATIONAL SOCIAL SYSTEMS
(2023)
Article
Mathematics, Applied
Ivan Eryganov, Jaroslav Hrdina
Summary: This paper presents an application of complex Clifford algebra in the representation of quantum prisoner's dilemma. The authors propose a novel modification of the Eisert-Lewenstein-Wilkens protocol to represent a repeated version of the quantum game, allowing the incorporation of entanglement into players' strategies. The use of complex Clifford algebra enables an intuitive representation of the protocol and efficient computation of the resulting payoff functions. The findings provide a new perspective on interpreting entanglement as a measure of information transition between game rounds.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Yu'e Wu, Zhipeng Zhang, Xinyu Wang, Ming Yan, Qingfeng Zhang, Shuhua Zhang
Summary: The study shows that the introduction of multigame enhances cooperation, and the coupling between the two sublayers of the network favors the spread of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Physics, Multidisciplinary
Jae Han Choi, Sungmin Lee, Jae Woo Lee
Summary: This study investigated the application of the prisoner's dilemma game in signed networks. The results showed that when the density of negative links is low, cooperation behavior is weakened; however, when the density of negative links is high, cooperation behavior is enhanced.
Article
Mathematics, Applied
Hirofumi Takesue
Summary: The study shows that playing evolutionary prisoner's dilemma games on dynamic two-layer multiplex networks with network dynamics can enhance cooperation, but significant asymmetry may arise when considering network multiplexity. This asymmetry can be eliminated with sufficiently fast link updating.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Thomas A. Wettergren
Summary: The replicator dynamics of two-player evolutionary games with delays are examined. We investigate the stability in situations where the delays on cost contributions and benefit contributions may be different. It is shown that increasing one delay can lead to instability, but further increases in the delay can bring back stability, followed by more instability, and so on. This is in contrast to the case where costs and benefits share a common delay, where only a simple destabilization occurs. A Hopf bifurcation analysis is employed to analyze the phenomenon for a general version of evolutionary games and conditions for stabilizing and destabilizing phenomena are identified. Specific examples of snowdrift game and division of labor game are used to illustrate the results and numerical examples are provided to validate the claims.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Yunsheng Deng, Jihui Zhang
Summary: Cooperation is considered crucial in evolution, and recent research has focused on the impact of memory mechanisms on human cooperative behavior. A two-layer interdependent network model was proposed, which showed that the density of cooperation is influenced by network parameters and memory length.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Interdisciplinary Applications
Zheng-Hong Deng, Zi-Ren Wang, Huan-Bo Wang, Yijie Huang
Summary: Informers play a significant role in cooperation behavior by labeling defectors and promoting cooperation. With an increasing proportion of informers, cooperation can be further enhanced, and there is an obvious threshold in the change of informers' proportion.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Sha Song, Qiuhui Pan, Wenqiang Zhu, Mingfeng He
Summary: In this study, the dual attribute strategy is introduced and simulated using snowdrift games to examine cooperative and defection behaviors among players. The results show that the dual attribute strategy is more likely to survive, and cooperation is more likely to exist when the cost-to-benefit ratios are smaller.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Information Systems
Haili Liang, Ying Cui, Xiaoqiang Ren, Xiaofan Wang
Summary: This paper investigates stochastic two-strategy evolutionary games with multiplicative noise interference and studies their stability, especially focusing on the impact of multiplicative noise on cooperation behavior in large well-mixed populations. The study establishes sufficient conditions on stochastic noise for stable equilibrium points of general two-strategy games to be almost sure exponentially stable (ASES). The stochastic Lyapunov framework is utilized to prove stochastic stability, with the key challenge lying in finding suitable Lyapunov functions.
INFORMATION SCIENCES
(2021)
Article
Computer Science, Artificial Intelligence
Yalun Li, Zhengyi Chai, Hongling Ma, Sifeng Zhu
Summary: This paper proposes an evolutionary algorithm based on the snowdrift game to solve the minimum weighted vertex cover (MWVC) problem. The algorithm combines the evolutionary algorithm framework with the snowdrift game to construct and improve the initial solution. Local search and global search are used to improve the initial solution, with a score function proposed in the local search stage. The experimental results on different networks show that the proposed algorithm is effective for weighted networks.
Article
Mathematics, Applied
Yuki Usui, Masahiko Ueda
Summary: In the repeated prisoner's dilemma game, players use reinforcement learning to obtain optimal memory strategies. The Win-stay Lose-shift strategy, the Grim strategy, and the strategy which always defects can form a symmetric equilibrium in the reinforcement learning process.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Zi-Ren Wang, Zheng-Hong Deng, Huan-Bo Wang, HuXiong Li Li, X. Fei-Wang
Summary: This study introduces an uneven resource distribution network model to investigate cooperative behavior among players. The findings indicate that defectors may initially occupy resource-rich areas but struggle to survive in hostile environments, while cooperators continue to thrive. Furthermore, cooperative behavior is promoted when resources are substantially depleted.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Multidisciplinary Sciences
Zhiqiang Gou, Ya Li
Summary: Decisions in dilemmas are influenced by multiple factors such as memory, reputation, reward, and punishment. Designing mechanisms to promote cooperation has become a popular research topic. However, previous studies have focused mainly on historical benefits and paid less attention to strategy stability and the role of memory. This study proposes a new strategy update rule to examine how the stability of historical strategy information influences cooperation in the prisoner's dilemma game.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Applied
Zhen Wang, Chaofan Li, Xing Jin, Hong Ding, Guanghai Cui, Lanping Yu
Summary: This study examined interdependent security games (IDS) models under three different attack scenarios, finding that individual behaviors are influenced by different factors under different network topologies, ultimately leading to the existence of a cluster effect.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
