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Axioms
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Advances in Logic and Game Theory
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Advances in Logic and Game Theory

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 31 July 2024 | Viewed by 6805

Special Issue Editor

Prof. Dr. Conrado Miguel Manuel García

E-Mail Website1 Website2
Guest Editor
Faculty of Statistics, Complutense University of Madrid, Puerta de Hierro, 1, 28040 Madrid, Spain
Interests: game theory; statistics

Special Issue Information

Dear Colleagues,

Strategic interaction analysis and logical and computational analysis can clarify each other. Therefore, it is interesting to promote research that provides illuminating answers, as well as offers insights at the interface of game theory and mathematical logic.

This Special Issue aims to make visible the state of the art today in logic and game theory by highlighting research on key issues.

The proposed articles should illuminate problems related to both logic and game theory and ideally address the widest possible audience. 

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following: 

  • Model games for formal language;
  • Beliefs in game theoretical analysis;
  • Equilibrium checking;
  • Concurrent games;
  • Logic and game theory. 

We look forward to receiving your contributions. 

Prof. Dr. Conrado Miguel Manuel García
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • model games for formal language
  • beliefs in game theoretical analysis
  • equilibrium checking
  • concurrent games
  • logic and game theory

Published Papers (6 papers)

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Research

21 pages, 872 KiB  
Article
Federated Learning Incentive Mechanism with Supervised Fuzzy Shapley Value
by Xun Yang, Shuwen Xiang, Changgen Peng, Weijie Tan, Yue Wang, Hai Liu and Hongfa Ding
Axioms 2024, 13(4), 254; https://doi.org/10.3390/axioms13040254 - 11 Apr 2024
Viewed by 352
Abstract
The distributed training of federated machine learning, referred to as federated learning (FL), is discussed in models by multiple participants using local data without compromising data privacy and violating laws. In this paper, we consider the training of federated machine models with uncertain [...] Read more.
The distributed training of federated machine learning, referred to as federated learning (FL), is discussed in models by multiple participants using local data without compromising data privacy and violating laws. In this paper, we consider the training of federated machine models with uncertain participation attitudes and uncertain benefits of each federated participant, and to encourage all participants to train the desired FL models, we design a fuzzy Shapley value incentive mechanism with supervision. In this incentive mechanism, if the supervision of the supervised mechanism detects that the payoffs of a federated participant reach a value that satisfies the Pareto optimality condition, the federated participant receives a distribution of federated payoffs. The results of numerical experiments demonstrate that the mechanism successfully achieves a fair and Pareto optimal distribution of payoffs. The contradiction between fairness and Pareto-efficient optimization is solved by introducing a supervised mechanism. Full article
(This article belongs to the Special Issue Advances in Logic and Game Theory)
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12 pages, 290 KiB  
Article
A Discrete Characterization of the Solvability of Equilibrium Problems and Its Application to Game Theory
by Maria Isabel Berenguer, Domingo Gámez, Ana Isabel Garralda-Guillem and Manuel Ruiz Galán
Axioms 2023, 12(7), 666; https://doi.org/10.3390/axioms12070666 - 05 Jul 2023
Viewed by 748
Abstract
We state a characterization of the existence of equilibrium in terms of certain finite subsets under compactness and transfer upper semicontinuity conditions. In order to derive some consequences on game theory—Nash equilibrium and minimax inequalities—we introduce a weak convexity concept. Full article
(This article belongs to the Special Issue Advances in Logic and Game Theory)
17 pages, 738 KiB  
Article
Federated Learning Incentive Mechanism Design via Shapley Value and Pareto Optimality
by Xun Yang, Shuwen Xiang, Changgen Peng, Weijie Tan, Zhen Li, Ningbo Wu and Yan Zhou
Axioms 2023, 12(7), 636; https://doi.org/10.3390/axioms12070636 - 27 Jun 2023
Cited by 1 | Viewed by 1371
Abstract
Federated learning (FL) is a distributed machine learning framework that can effectively help multiple players to use data to train federated models while complying with their privacy, data security, and government regulations. Due to federated model training, an accurate model should be trained, [...] Read more.
Federated learning (FL) is a distributed machine learning framework that can effectively help multiple players to use data to train federated models while complying with their privacy, data security, and government regulations. Due to federated model training, an accurate model should be trained, and all federated players should actively participate. Therefore, it is crucial to design an incentive mechanism; however, there is a conflict between fairness and Pareto efficiency in the incentive mechanism. In this paper, we propose an incentive mechanism via the combination of the Shapley value and Pareto efficiency optimization, in which a third party is introduced to supervise the federated payoff allocation. If the payoff can reach Pareto optimality, the federated payoff is allocated by the Shapley value method; otherwise, the relevant federated players are punished. Numerical and simulation experiments show that the mechanism can achieve fair payoff allocation and Pareto optimality payoff allocation. The Nash equilibrium of this mechanism is formed when Pareto optimality payoff allocation is achieved. Full article
(This article belongs to the Special Issue Advances in Logic and Game Theory)
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18 pages, 320 KiB  
Article
Characteristic Function of Maxmax Defensive-Equilibrium Representation for TU-Games with Strategies
by Chenwei Liu, Shuwen Xiang and Yanlong Yang
Axioms 2023, 12(6), 521; https://doi.org/10.3390/axioms12060521 - 25 May 2023
Viewed by 767
Abstract
In this paper, we propose a characteristic function of the maxmax defensive-equilibrium representation that maps every TU-game with strategies to a TU-game. This characteristic function is given by a two-step procedure in which each of any two complementary coalitions successively selects the equilibrium [...] Read more.
In this paper, we propose a characteristic function of the maxmax defensive-equilibrium representation that maps every TU-game with strategies to a TU-game. This characteristic function is given by a two-step procedure in which each of any two complementary coalitions successively selects the equilibrium in a way that maximizes its utility. We then investigate the properties of this characteristic function and present the relations of the cores under three characteristic functions. Finally, as applications of our findings, we provide a firm production advertising game, a supply chain network game, a cost game with strategies, and a Cournot game. Full article
(This article belongs to the Special Issue Advances in Logic and Game Theory)
15 pages, 322 KiB  
Article
Cooperative Games Based on Coalition Functions in Biform Games
by Chenwei Liu, Shuwen Xiang, Yanlong Yang and Enquan Luo
Axioms 2023, 12(3), 296; https://doi.org/10.3390/axioms12030296 - 13 Mar 2023
Cited by 1 | Viewed by 1114
Abstract
In this paper, we try to study a class of biform games with the coalition function from the cooperation of players. For this purpose, we interpret the biform games as cooperative games by defining a characteristic function of minimax representation based on the [...] Read more.
In this paper, we try to study a class of biform games with the coalition function from the cooperation of players. For this purpose, we interpret the biform games as cooperative games by defining a characteristic function of minimax representation based on the coalition function and giving the core and Shapley value as cooperative solutions. The relations between the coalition function and the characteristic function are investigated in terms of additivity and convexity, and the properties associated with the characteristic function, such as individual rationalities and cores, are compared with the corresponding results. The relations among the solutions of the normal-form game, biform game, and cooperative game are discussed with several examples. Full article
(This article belongs to the Special Issue Advances in Logic and Game Theory)
16 pages, 318 KiB  
Article
Communication in Weighted Networks: A Game Theoretic Approach
by Elena C. Gavilán, Conrado Manuel and Daniel Martín
Axioms 2023, 12(2), 180; https://doi.org/10.3390/axioms12020180 - 09 Feb 2023
Viewed by 927
Abstract
In this paper we generalize the allocation rule (point solution or value) known as the mixed value by introducing the weighted mixed value.The proposed solution assigns value in graph games where players, and/or links, have weights representing asymmetries of the players, and different [...] Read more.
In this paper we generalize the allocation rule (point solution or value) known as the mixed value by introducing the weighted mixed value.The proposed solution assigns value in graph games where players, and/or links, have weights representing asymmetries of the players, and different flows, lengths, emotional intensities, trust in the transmission of the information, etc. in the links. We present several characterizations of this value using properties, such as mixed component efficiency, weighted mixed fairness, weighted balanced contributions and weighted balanced link contributions. These properties were inspired by the classical properties used to characterize the Myerson value and the position value. Full article
(This article belongs to the Special Issue Advances in Logic and Game Theory)
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