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Mathematics
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Game Theory and Complex Networks
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Game Theory and Complex Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 5473

Special Issue Editor

Dr. Yichao Zhang

E-Mail Website
Guest Editor
Department of Computer Science and Technology, Tongji University, Shanghai, China
Interests: complex networks; game theory; rumor spreading

Special Issue Information

Dear Colleagues,

From public goods to information gathering, a player's payoffs depend on his or her actions and the actions of their neighbors in gaming networks. This issue provides an opportunity to analyze strategic interactions and mine the origins of cooperation among agents, including humans. Owing to the broad attention in mathematics and engineering communities, strategy-updating mechanisms, network structures, game behaviors, temporal information, incomplete gaming information, etc., are the focus of this Special Issue. The primary purpose of this Special Issue is to disclose the latest progress, unique perspectives, and new methods in the field and encourage original works.

Dr. Yichao Zhang
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • game theory
  • complex networks

Published Papers (5 papers)

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Research

15 pages, 3196 KiB  
Article
Short Memory-Based Human Strategy Modeling in Social Dilemmas
by Xiang-Hao Yang, Hui-Yun Huang, Yi-Chao Zhang, Jia-Sheng Wang, Ji-Hong Guan and Shui-Geng Zhou
Mathematics 2023, 11(12), 2709; https://doi.org/10.3390/math11122709 - 15 Jun 2023
Viewed by 679
Abstract
Human decision-making processes are complex. It is thus challenging to mine human strategies from real games in social networks. To model human strategies in social dilemmas, we conducted a series of human subject experiments in which the temporal two-player non-cooperative games among 1092 [...] Read more.
Human decision-making processes are complex. It is thus challenging to mine human strategies from real games in social networks. To model human strategies in social dilemmas, we conducted a series of human subject experiments in which the temporal two-player non-cooperative games among 1092 players were intensively investigated. Our goal is to model the individuals’ moves in the next round based on the information observed in each round. Therefore, the developed model is a strategy model based on short-term memory. Due to the diversity of user strategies, we first cluster players’ behaviors to aggregate them with similar strategies for the following modeling. Through behavior clustering, our observations show that the performance of the tested binary strategy models can be highly promoted in the largest behavior groups. Our results also suggest that no matter whether in the classical mode or the dissipative mode, the influence of individual accumulated payoffs on individual behavior is more significant than the gaming result of the last round. This result challenges a previous consensus that individual moves largely depend on the gaming result of the last round. Therefore, our model provides a novel perspective for understanding the evolution of human altruistic behavior. Full article
(This article belongs to the Special Issue Game Theory and Complex Networks)
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26 pages, 5850 KiB  
Article
Evolutionary Game of Vaccination Considering Both Epidemic and Economic Factors by Infectious Network of Complex Nodes
by Bing Li and Ziye Xiang
Mathematics 2023, 11(12), 2697; https://doi.org/10.3390/math11122697 - 14 Jun 2023
Viewed by 1056
Abstract
Vaccines are recognized as an effective way to control the spread of epidemics. It should be noted that the vaccination of a population is influenced not only by the infectiousness of a disease but also the vaccination strategy, such as the cost of [...] Read more.
Vaccines are recognized as an effective way to control the spread of epidemics. It should be noted that the vaccination of a population is influenced not only by the infectiousness of a disease but also the vaccination strategy, such as the cost of vaccination. An accurate prediction model is helpful in forecasting the most likely trend to support smart decisions. In order to solve this problem, a model of epidemic spread dynamics is proposed, which is called the Susceptible–Infected–Vaccinated with vaccine A–Vaccinated with vaccine B–Recovered (SIVAVBR) model. This model assesses the competition between two vaccines in terms of economic cost and protection effectiveness in an open-market economy. The optimization process of individual vaccination decision-making was studied in an evolutionary game. In addition, a novel network containing environmental nodes and individual nodes was used to simulate the increase in infection probability caused by aggregation. Using the mean-field approach, the existence and stability of the disease-free equilibrium point and the endemic equilibrium point were demonstrated. Numerous simulations were further carried out to examine the relationship between the basic reproduction number and epidemic dynamics. The results reveal that immunization hesitation reduces the immunity level of the entire population. It is important to improve vaccine efficiency and affordability for manufacturers to become more competitive. Establishing the core individuals in the network is also a means of quickly occupying the market. Full article
(This article belongs to the Special Issue Game Theory and Complex Networks)
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11 pages, 2098 KiB  
Article
The Evolution of Cooperation in Multigames with Uniform Random Hypergraphs
by Haozheng Xu, Yiwen Zhang, Xing Jin, Jingrui Wang and Zhen Wang
Mathematics 2023, 11(11), 2409; https://doi.org/10.3390/math11112409 - 23 May 2023
Cited by 2 | Viewed by 1047
Abstract
How to explain the emergence of cooperative behavior remains a significant problem. As players may hold diverse perceptions on a particular dilemma, the concept of multigames has been introduced. Therefore, a multigame is studied within various binary networks. Since group structures are common [...] Read more.
How to explain the emergence of cooperative behavior remains a significant problem. As players may hold diverse perceptions on a particular dilemma, the concept of multigames has been introduced. Therefore, a multigame is studied within various binary networks. Since group structures are common in human society and a person can participate in multiple groups, this paper studies an evolutionary multigame with high-order interaction properties. For this purpose, a uniform random hypergraph is adopted as the network structure, allowing players to interact with all nodes in the same hyperedge. First, we investigate the effect of the multigame payoff matrix differences on the evolution of cooperation and find that increasing the differences in the payoff matrix promotes cooperation on the hypergraph network. Second, we discover that an increase in the average hyperdegree of the hypergraph network promotes network reciprocity, wherein high-hyperdegree nodes influence surrounding nodes to form a cooperator cluster. Conversely, groups with a low hyperdegree are more susceptible to betrayal, leading to a decline in cooperation. Full article
(This article belongs to the Special Issue Game Theory and Complex Networks)
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23 pages, 836 KiB  
Article
Observability of Discrete-Time Two-Time-Scale Multi-Agent Systems with Heterogeneous Features under Leader-Based Architecture
by Mengqi Gu and Guo-Ping Jiang
Mathematics 2023, 11(8), 1907; https://doi.org/10.3390/math11081907 - 18 Apr 2023
Viewed by 790
Abstract
This paper investigates the observability of discrete-time two-time-scale multi-agent systems with heterogeneous features under leader–follower architecture. First, a singular perturbation difference model for the discussed system is established based on consensus agreement. Second, to eliminate the numerical ill-posed problem that may arise from [...] Read more.
This paper investigates the observability of discrete-time two-time-scale multi-agent systems with heterogeneous features under leader–follower architecture. First, a singular perturbation difference model for the discussed system is established based on consensus agreement. Second, to eliminate the numerical ill-posed problem that may arise from the singularly perturbed small parameter that distinguishes different time scales in the observability analysis, the order of the system model is reduced using the boundary layer theory of the singular perturbation system to obtain a slow-time-scale subsystem and a fast-time-scale subsystem. Then, based on the matrix theory, some algebraic and graphical features that guarantee the observability of the system are obtained. Finally, the validity of the theoretical results is verified by a numerical example. Full article
(This article belongs to the Special Issue Game Theory and Complex Networks)
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21 pages, 516 KiB  
Article
Toward Zero-Determinant Strategies for Optimal Decision Making in Crowdsourcing Systems
by Jiali Wang, Changbing Tang, Jianquan Lu and Guanrong Chen
Mathematics 2023, 11(5), 1153; https://doi.org/10.3390/math11051153 - 26 Feb 2023
Viewed by 1006
Abstract
The crowdsourcing system is an internet-based distributed problem-solving and production organization model, which has been applied in human–computer interaction, databases, natural language processing, machine learning and other fields. It guides the public to complete some tasks through specific strategies and methods. However, rational [...] Read more.
The crowdsourcing system is an internet-based distributed problem-solving and production organization model, which has been applied in human–computer interaction, databases, natural language processing, machine learning and other fields. It guides the public to complete some tasks through specific strategies and methods. However, rational and selfish workers in crowdsourcing systems will submit solutions of different qualities in order to maximize their own benefits. Therefore, how to choose optimal strategies for selfish workers to maximize their benefits is important and crucial in such a scenario. In this paper, we propose a decision optimization method with incomplete information in a crowdsourcing system based on zero-determinant (ZD) strategies to help workers make optimal decisions. We first formulate the crowdsourcing problem, where workers have “winner-takes-all” rules as an iterated game with incomplete information. Subsequently, we analyze the optimal decision of workers in crowdsourcing systems in terms of ZD strategies, for which we find conditions to reach the maximum payoff of a focused worker. In addition, the analysis helps understand what solutions selfish workers will submit under the condition of having incomplete information. Finally, numerical simulations illustrate the performances of different strategies and the effects of the parameters on the payoffs of the focused worker. Full article
(This article belongs to the Special Issue Game Theory and Complex Networks)
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