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Applications of Game Theory with Mathematical Methods

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A special issue of Games (ISSN 2073-4336). This special issue belongs to the section "Algorithmic and Computational Game Theory".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 8981

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Special Issue Editor

Dr. Yllka Velaj

E-Mail Website
Guest Editor

Faculty of Computer Science, University of Vienna, 1090 Vienna, Austria
Interests: network analysis; graph algorithms; algorithms and complexity; algorithmic game theory; knowledge discovery; data mining; clustering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue of Games is dedicated to decision making, game theory and economic modeling. Game theory is a very relevant field, which has only gained importance as it has aimed to find optimal solutions to situations of conflict and represent the theory of independent and interdependent decision making.

We invite game theoretical and experimental contributions on the foundations, development, analysis, and applications of game theory. Potential topics include, but are not limited to, the analysis of multi-agent systems; solution concepts in game theory; mechanism design; coalitions, coordination, and collective action; economic paradigms; cooperative and non-cooperative games; social choice; and network games. We list below further keywords that may help to identify suitable topics for the Special Issue.

Dr. Yllka Velaj
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. Games 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 1600 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

multi-agent systems
economic and computation
solution concepts in game theory
algorithmic mechanism design
economic paradigms
cooperative and non-cooperative algorithmic game theory
social choice and voting
network games

Published Papers (7 papers)

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Research

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20 pages, 1016 KiB

Open AccessArticle

Quantum Tapsilou—A Quantum Game Inspired by the Traditional Greek Coin Tossing Game Tapsilou

by Kalliopi Kastampolidou and Theodore Andronikos

Games 2023, 14(6), 72; https://doi.org/10.3390/g14060072 - 20 Nov 2023

Viewed by 1248

Abstract

This paper introduces a new quantum game called Quantum Tapsilou that is inspired by the classical traditional Greek coin tossing game tapsilou. The new quantum game, despite its increased complexity and scope, retains the most important characteristic of the traditional game. In the [...] Read more.

\frac{1}{4}

probability to win. The quantum version retains this characteristic feature, which is that both players have the same probability to win, but only now this probability varies considerably and depends on previous moves and choices. The two most important novelties of Quantum Tapsilou can be attributed to its implementation of entanglement via the use of rotation gates instead of Hadamard gates, which generates Bell-like states with unequal probability amplitudes, and the integral use of groups. In Quantum Tapsilou both players agree on a specific cyclic rotation group of order n, for some sufficiently large n. The game is based on the chosen group, in the sense that both players will draw their moves from its elements. More specifically, both players will pick rotations from this group to realize their actions using the corresponding

R_{y}

rotation gates. In the Quantum Tapsilou game, it is equally probable for both players to win. This fact is in accordance with a previous result in the literature showing that quantum games where both players choose their actions from the same group, exhibit perfect symmetry by providing each player with the possibility to pick the move that counteracts the other player’s action. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

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Figure 1

10 pages, 365 KiB

Open AccessCommunication

A Discrete-Time Homing Problem with Two Optimizers

by Mario Lefebvre

Games 2023, 14(6), 68; https://doi.org/10.3390/g14060068 - 27 Oct 2023

Viewed by 1011

Abstract

A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk

{X_{n}, n = 0, 1, \dots}

in the continuation region [...] Read more.

A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk

{X_{n}, n = 0, 1, \dots}

in the continuation region

C : = {1, 2, \dots}

, and the second player seeks to maximize the survival time in C. The process starts at

X_{0} = x > 0

and the game ends the first time

X_{n} \leq 0

. An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

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Figure 1

19 pages, 356 KiB

Open AccessArticle

Game Theoretic Foundations of the Gately Power Measure for Directed Networks

by Robert P. Gilles and Lina Mallozzi

Games 2023, 14(5), 64; https://doi.org/10.3390/g14050064 - 26 Sep 2023

Viewed by 1055

Abstract

We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players—constituting a hierarchical network. The power distribution embedded within a hierarchical network can be represented through appropriate TU-games. We investigate the properties of these TU-representations and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a core power gauge, investigate the relationship of the Gately with the

β

-measure, and construct an axiomatisation of the Gately measure. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

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Figure 1

27 pages, 504 KiB

Open AccessArticle

A Two-Player Resource-Sharing Game with Asymmetric Information

by Mevan Wijewardena and Michael J. Neely

Games 2023, 14(5), 61; https://doi.org/10.3390/g14050061 - 17 Sep 2023

Viewed by 1002

Abstract

This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each player has knowledge of the reward realizations of different subsets of the resources. If both players choose the same resource, the reward is divided equally between them, whereas if they choose different resources, each player gains the full reward of the resource. We first implement the iterative best response algorithm to find an

ϵ

-approximate Nash equilibrium for this game. This method of finding a Nash equilibrium may not be desirable when players do not trust each other and place no assumptions on the incentives of the opponent. To handle this case, we solve the problem of maximizing the worst-case expected utility of the first player. The solution leads to counter-intuitive insights in certain special cases. To solve the general version of the problem, we develop an efficient algorithmic solution that combines online convex optimization and the drift-plus penalty technique. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

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21 pages, 1743 KiB

Open AccessArticle

Risk-Averse and Self-Interested Shifts in Groups in Both Median and Random Rules

by Yoshio Kamijo and Teruyuki Tamura

Games 2023, 14(1), 16; https://doi.org/10.3390/g14010016 - 13 Feb 2023

Viewed by 1296

Abstract

The purpose of this study was to determine whether attitudes toward risk and altruism are affected by being in a group or being alone. In contrast to previous economic research on group decision-making, we excluded the effects of group informal discussions, which are thought to be a “black box” when individuals make decisions in a group. In this regard, the subjects in our experiment were only requested to show their faces to the other members, without further communication. Moreover, we adopted two collective decision rules, i.e., the median rule and the random rule, which provide the truth-telling mechanism. In the experiments of both anonymous investment and donation, we found that the subjects who made decisions in a group offered significantly lower amounts than those who made decisions alone, after controlling for individuals’ risk and altruistic preferences. The findings imply that people are more risk-averse and self-interested when they are in a group, regardless of which collective decision rules are adopted. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

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18 pages, 306 KiB

Open AccessArticle

Differential Game-Theoretic Models of Cournot Oligopoly with Consideration of the Green Effect

by Guennady Ougolnitsky and Anatoly Usov

Games 2023, 14(1), 14; https://doi.org/10.3390/g14010014 - 30 Jan 2023

Cited by 2 | Viewed by 1271

Abstract

We built and investigated analytically and numerically a differential game model of Cournot oligopoly with consideration of pollution for the general case and the case of symmetrical agents. We conducted a comparative analysis of selfish agents’ behavior (a differential game in normal form), their hierarchical organization (differential Stackelberg games), and cooperation (optimal control problem) using individual and collective indices of relative efficiency. The same analysis wasperformed for the models with the green effect when players chose both output volumes and environmental protection efforts. We used the Pontryagin maximum principle for analytical investigation and the method of qualitatively representative scenarios in simulation modeling for numerical calculations. This method allows for reducing the number of computer simulations, providing sufficient precision. As a result of the comparative analysis, systems of collective and individual preferences were obtained. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

Review

Jump to: Research

13 pages, 377 KiB

Open AccessReview

Matrix-Based Method for the Analysis and Control of Networked Evolutionary Games: A Survey

by Xinrong Yang, Zhenping Geng and Haitao Li

Games 2023, 14(2), 22; https://doi.org/10.3390/g14020022 - 28 Feb 2023

Viewed by 1422

Abstract

In this paper, a detailed survey is presented for the analysis and control of networked evolutionary games via the matrix method. The algebraic form of networked evolutionary games is firstly recalled. Then, some existing results on networked evolutionary games are summarized. Furthermore, several generalized forms of networked evolutionary games are reviewed, including networked evolutionary games with time delay, networked evolutionary games with bankruptcy mechanism, networked evolutionary games with time-varying networks, and random evolutionary Boolean games. The computational complexity of general networked evolutionary games is still challenging, which limits the application of the matrix method to large-scale networked evolutionary games. Future works are finally presented in the conclusion. Full article

(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)

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