Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
3.5
2.4
Journals
Mathematics
Special Issues
Cooperative Game Theory and Mathematical Structures
share announcement

Cooperative Game Theory and Mathematical Structures

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

Deadline for manuscript submissions: closed (31 August 2022) | Viewed by 8861

Special Issue Editor

Prof. Dr. Andrés Jiménez Losada

E-Mail Website
Guest Editor
Applied Mathematics II, Universidad de Sevilla, Sevilla, Spain
Interests: game theory; cooperative games; decision theory; fuzzy sets; fuzzy relations; formal contexts; antimatroids; matroids; convex geometries; graphs; fuzzy graphs

Special Issue Information

Dear Colleauges,

The theory of cooperative games studies situations of cooperation between a group of agents (human or not), exploring the formation of groups (coalitions), the distribution of benefits, or costs produced by the collaboration between these agents or the elaboration of rankings between them. In recent years, it has developed very widely in two main aspects. On the one hand, the introduction of various mathematical structures in this theory has allowed the representation of coalition systems and the relations between players and payments to be received in a much more precise way. In this way, situations of cooperation in environments of asymmetry or uncertainty can be analysed. On the other hand, the applications have reached practically all aspects of science and engineering. For these reasons, this issue aims to compile new advances in the introduction and application of mathematical structures in cooperative games.

Prof. Dr. Andrés Jiménez Losada
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

  • Cooperative game
  • Networks
  • Fuzzy and Rough sets
  • Allocation rules
  • Combinatorial structures
  • Applications of cooperative games

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

9 pages, 272 KiB  
Article
An Axiomatization of the Value α for Games Restricted by Augmenting Systems
by Guangming Wang, Zeguang Cui and Erfang Shan
Mathematics 2022, 10(15), 2803; https://doi.org/10.3390/math10152803 - 07 Aug 2022
Cited by 1 | Viewed by 785
Abstract
The value α for augmenting structures was introduced and axiomatically characterized by Algaba, Bilbao and Slikker. In this paper, we provide a new axiomatization of the value α for augmenting structures by using marginality for augmenting structures and the standard axioms of component [...] Read more.
The value α for augmenting structures was introduced and axiomatically characterized by Algaba, Bilbao and Slikker. In this paper, we provide a new axiomatization of the value α for augmenting structures by using marginality for augmenting structures and the standard axioms of component efficiency, equal treatment of necessary players and loop-null. Full article
(This article belongs to the Special Issue Cooperative Game Theory and Mathematical Structures)
21 pages, 337 KiB  
Article
Preplay Negotiations with Unconditional Offers of Side Payments in Two-Player Strategic-Form Games: Towards Non-Cooperative Cooperation
by Valentin Goranko
Mathematics 2022, 10(14), 2518; https://doi.org/10.3390/math10142518 - 20 Jul 2022
Viewed by 1244
Abstract
I consider strategic-form games with transferable utility extended with a phase of negotiations before the actual play of the game, where players can exchange a series of alternating (turn-based) unilaterally binding offers to each other for incentive payments of utilities after the play, [...] Read more.
I consider strategic-form games with transferable utility extended with a phase of negotiations before the actual play of the game, where players can exchange a series of alternating (turn-based) unilaterally binding offers to each other for incentive payments of utilities after the play, conditional only on the recipients playing the strategy indicated in the offer. Every such offer transforms the game payoff matrix by accordingly transferring the offered amount from the offering player’s payoff to the recipient’s in all outcomes where the indicated strategy is played by the latter. That exchange of offers generates an unbounded-horizon, extensive-form preplay negotiations game, which is the focus of this study. In this paper, I study the case where the players assume that their opponents can terminate the preplay negotiations phase at any stage. Consequently, in their negotiation strategies, the players are guided by myopic rationality reasoning and aim at optimising each of their offers. The main results and findings include a concrete algorithmic procedure for computing players’ best offers in the preplay negotiations phase and using it to demonstrate that these negotiations can generally lead to substantial improvement of the payoffs for both players in the transformed game, but they do not always lead to optimal outcomes, as one might expect. Full article
(This article belongs to the Special Issue Cooperative Game Theory and Mathematical Structures)
►▼ Show Figures

Figure 1

15 pages, 615 KiB  
Article
A Value for Graph-Restricted Games with Middlemen on Edges
by Antonio C. Alarcón, José M. Gallardo and Andrés Jiménez-Losada
Mathematics 2022, 10(11), 1856; https://doi.org/10.3390/math10111856 - 28 May 2022
Viewed by 1456
Abstract
In a cooperative game with a communication structure, a graph describes the communication possibilities of the players, which are represented by the nodes. We introduce a variation of this model by assuming that each edge in the communication graph represents an agent. These [...] Read more.
In a cooperative game with a communication structure, a graph describes the communication possibilities of the players, which are represented by the nodes. We introduce a variation of this model by assuming that each edge in the communication graph represents an agent. These agents simply act as intermediaries, but since they are essential for the cooperation and, consequently, for revenue generation, they will claim their share of the profit. We study this new model of games with a communication structure and introduce an allocation rule for these games. The motivation for analyzing this type of problem is based on the construction of a risk index for the different elements of an internal network. Full article
(This article belongs to the Special Issue Cooperative Game Theory and Mathematical Structures)
►▼ Show Figures

Figure 1

13 pages, 502 KiB  
Article
Public Provision of Goods and Services under Cost Uncertainty: The Government’s Bureaucratic Organization
by Giovanni Di Bartolomeo, Silvia Fedeli and Michele Santoni
Mathematics 2022, 10(1), 77; https://doi.org/10.3390/math10010077 - 27 Dec 2021
Viewed by 1708
Abstract
The digital transition is a challenge that developed countries are currently facing. The transition process is associated with different degrees of uncertainty, which are particularly relevant for changes that have to do with the provision of goods and services produced by public administrations. [...] Read more.
The digital transition is a challenge that developed countries are currently facing. The transition process is associated with different degrees of uncertainty, which are particularly relevant for changes that have to do with the provision of goods and services produced by public administrations. Our paper uses a partial equilibrium model to study the effects of uncertainty on the public provision of goods and services produced by bureaucratic agencies, including the incentive of the government to consolidate production. We assume that bureaucratic agencies may play either a cooperative game with each other and a non-cooperative game against the government (i.e., a consolidated bureaucracy) or a non-cooperative game with each other and against the government (i.e., competing bureaus). Both the government and the bureaus face tradeoffs between maximizing the electorate preferences and extracting some political and/or bureaucratic rents. We find that a cooperative (competitive) bureaucratic solution depends on the nature of the goods produced. We find that costs’ uncertainty affects the level of public production and the way the policymakers extract their rents. Full article
(This article belongs to the Special Issue Cooperative Game Theory and Mathematical Structures)
►▼ Show Figures

Figure 1

29 pages, 488 KiB  
Article
A New Edge Betweenness Measure Using a Game Theoretical Approach: An Application to Hierarchical Community Detection
by Daniel Gómez, Javier Castro, Inmaculada Gutiérrez and Rosa Espínola
Mathematics 2021, 9(21), 2666; https://doi.org/10.3390/math9212666 - 21 Oct 2021
Cited by 3 | Viewed by 1534
Abstract
In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the [...] Read more.
In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results. Full article
(This article belongs to the Special Issue Cooperative Game Theory and Mathematical Structures)
►▼ Show Figures

Figure 1

14 pages, 264 KiB  
Article
Axiomatic Results for Weighted Allocation Rules under Multiattribute Situations
by Yu-Hsien Liao
Mathematics 2021, 9(6), 617; https://doi.org/10.3390/math9060617 - 15 Mar 2021
Viewed by 998
Abstract
In many interactive environments, operators may have to deal with different work objectives at the same time. In a realistic context, such as differences in the target type to be addressed, or changes in the behavior of other operators, operators may therefore have [...] Read more.
In many interactive environments, operators may have to deal with different work objectives at the same time. In a realistic context, such as differences in the target type to be addressed, or changes in the behavior of other operators, operators may therefore have to cope with by adopting different work levels (strategies) at any given time. On the other hand, the importance or influence brought by operators may vary depending on many subjective and objective factors, such as the size of the constituency represented by a congressman, and the bargaining power of a business personnel which may vary. Therefore, it is reasonable that weights are apportioned to operators and arbitrary usability should be distributed according to these weights under various working levels and multiattribute situations. In pre-existing results for allocation rules, weights might be always apportioned to the “operators” or the “levels” to modify the differences among the operators or its working levels respectively. By applying weights to the operators and its working levels (strategies) simultaneously, we adopt the maximal marginal variations among working level (strategy) vectors to propose an allocation rule under multiattribute situations. Furthermore, we introduce some axiomatic outcomes to display the rationality for this weighted allocation rule. By replacing weights to be maximal marginal variations, a generalized index is also introduced. Full article
(This article belongs to the Special Issue Cooperative Game Theory and Mathematical Structures)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop