Game Theory and Applications

Topic Information

Dear Colleagues,

Game theory, which is the study of strategic decision making, was first developed as a branch of microeconomics. Since the seminal work of John Von Neumann, John Nash, and others, it has been recognised that there is an optimal strategy in the context of complex interactions (games) between two or more parties (players) that can lead to a predictable outcome (payoff). In practical situations, this outcome can often be quantitative and amenable to arithmetic operations (cost, number of infected people, number of vaccinated people, etc.), but it can be qualitative in nature (such as risk, readiness level, health state, etc.). A typical game defined in game theory has two or more players, a set of strategies available to these players, and a corresponding set of pay-off values (sometimes called utility values) for each player (which are, in the case of two-player games, often presented as a pay-off matrix). Game theory can be classified into two broad domains: non-cooperative game theory and cooperative game theory. Game Theory has become one of the conventional theoretical frameworks to model important decision-making processes in many aspects of life. In recent years, game theory has been adopted in diverse fields of study, such as evolutionary biology, sociology, psychology, political science and computer science. Game theory is used to study many phenomena and behavioural patterns in human societies and socio-economical systems, such as the emergence of and means of sustaining cooperation in communities and organisations, modelling of unethical or criminal behaviour, or the decision-making processes involved in vaccination against epidemics. Game Theory provides insight into peculiar behavioural interactions such as cooperative interactions within groups of animals, the bargaining and exchange in a marriage, or the incentivisation of Scottish salmon farmers. Game theory has gained such wide applicability due to the prevalence of strategic decision-making scenarios across different disciplines. The applications of game theory have become so diverse that it now spans many major disciplines. As such, it is eminently suitable to be defined as a ‘Topic’, which covers several MDPI journals. Therefore, we are proposing that ‘Game Theory and Applications’ is made a ‘Topic’ across the following four MDPI journals: [Algorithms, Games, Information, Mathematics]. As the topic editor, on behalf of my colleagues in the Topic board, I seek articles that could enrich this Topic collection. Papers can be one of the following types: [Articles, Reviews, etc.].

Dr. Mahendra Piraveenan
Dr. Samit Bhattacharrya
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Algorithms algorithms	1.8	4.1	2008	18.9 Days	CHF 1600
Games games	0.6	1.6	2010	24.8 Days	CHF 1600
Information information	2.4	6.9	2010	16.4 Days	CHF 1600
Mathematics mathematics	2.3	4.0	2013	18.3 Days	CHF 2600

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Published Papers (20 papers)

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19 pages, 832 KiB  

Open AccessArticle

Characterizing Manipulation via Machiavellianism

by Jacqueline Sanchez-Rabaza, Jose Maria Rocha-Martinez and Julio B. Clempner

Mathematics 2023, 11(19), 4143; https://doi.org/10.3390/math11194143 - 30 Sep 2023

Cited by 1 | Viewed by 1470

Abstract

Machiavellianism refers to the propensity of taking advantage of people within a society. Machiavellians have reputations for being cunning and competitive. They are also skilled long-term strategists and planners. Other than their “victories,” there are no other successful conclusions for them. The belief [...] Read more.

Machiavellianism refers to the propensity of taking advantage of people within a society. Machiavellians have reputations for being cunning and competitive. They are also skilled long-term strategists and planners. Other than their “victories,” there are no other successful conclusions for them. The belief component of Machiavellianism includes cynical views of human nature (e.g., manipulated and manipulating individuals), interpersonal exploitation as a technique (e.g., strategic thinking), and a lack of traditional morality that would forbid their behaviors (e.g., immoral behaviors). This paper focuses on a game that involves manipulation. The game was conceptualized using the best and worst Nash equilibrium points as part of our contribution. We constrained the problem to homogeneous, finite, ergodic, and controllable Bayesian–Markov games. Machiavellian players pretended to be in one state when they were actually in another. Moreover, they pretended to perform one action while actually playing another. All Machiavellian individuals engaged in some form of interpersonal manipulation. Manipulating players exhibited a higher preference compared to manipulated participants. The Pareto frontier is defined as the line where manipulating players play the best Nash equilibrium and manipulated players play the worst Nash equilibrium. It is also considered a sequential Bayesian–Markov manipulation game involving multiple manipulating players and manipulated players. Finally, a tractable characterization of the manipulation equilibrium results is provided. To guarantee that the game’s solution converged into a singular solution, we used Tikhonov’s penalty regularization method. A numerical example describes the results of our model. Full article

(This article belongs to the Topic Game Theory and Applications)

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22 pages, 3076 KiB  

Open AccessArticle

Channel Competition and Coordination of a Dual-Channel Supply Chain under Interval Demand

by Chunhua Tang, Erbao Cao and Zhanwen Shi

Mathematics 2023, 11(12), 2720; https://doi.org/10.3390/math11122720 - 15 Jun 2023

Cited by 1 | Viewed by 2128

Abstract

Interval demand is becoming more common than ever before, since the variation bounds of uncertain demand are only required in practice, and they could be obtained through only a small amount of uncertain information. The goal of this paper is to analyze the [...] Read more.

Interval demand is becoming more common than ever before, since the variation bounds of uncertain demand are only required in practice, and they could be obtained through only a small amount of uncertain information. The goal of this paper is to analyze the optimal decision and coordination of a competitive dual-channel supply chain under an interval uncertain demand. For this purpose, we establish a centralized decision model and a wholesale price contract model under both interval demand and channel competition, respectively. Meanwhile, both the satisfaction degree of interval and the order relation of interval number are proposed to convert interval uncertain optimization problems to deterministic ones. Then, we derive the optimal pricing decisions, ordering quantities, and performances of partners and the supply chain system. Meanwhile, a revenue sharing contract is proposed to coordinate the competitive dual-channel supply chain under interval demand. Moreover, we found that the bounds of interval demand and channel sensitivities affect the optimal strategies and revenue sharing contract under interval uncertainty. Finally, we present a numerical analysis to illustrate the proposed results in this paper and conduct sensitivity analyses. The findings of this paper provide important references for decision makers and managers to make scientific decisions in an interval uncertain environment. Full article

(This article belongs to the Topic Game Theory and Applications)

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30 pages, 2728 KiB  

Open AccessArticle

Alternative Method to Resolve the Principal–Principal Conflict—A New Perspective Based on Contract Theory and Negotiation

by Yuxun Zhou, Mohammad Mafizur Rahman, Rasheda Khanam and Brad R. Taylor

Mathematics 2023, 11(2), 442; https://doi.org/10.3390/math11020442 - 13 Jan 2023

Cited by 1 | Viewed by 2129

Abstract

Liquidated damages mechanisms have been analyzed from a legal perspective and applied to real-world contracts. Due to the lack of application of LDs to common agency theory, this research explores whether the liquidated damages mechanism can resolve principal–principal conflicts under common agency. We [...] Read more.

Liquidated damages mechanisms have been analyzed from a legal perspective and applied to real-world contracts. Due to the lack of application of LDs to common agency theory, this research explores whether the liquidated damages mechanism can resolve principal–principal conflicts under common agency. We combine the moral hazard model of common agency with non-cooperative dynamic game theory to analyze the influence of the liquidated damages mechanism on the agent and principals under the condition of complete information and incomplete information. We find that liquidated damages are the key factors affecting the optimal contract between the principal and agent. Since the agent does not terminate the current contract, a principal–principal conflict arises when another principal wishes to enter into a new contract with the common agent. We find that the agent terminates the existing contract and signs a new one with another principal. The injured party requires liquidated damages from the breaching party. Therefore, they will negotiate the number of liquidated damages. Liquidated damages cause the bargaining game to generate a unique subgame perfect Nash equilibrium and sequential equilibrium. We prove that only when liquidated damages belong to a specific interval does a mechanism generating the Pareto optimal solutions to solve the principal–principal conflicts under common agency exist. A common way to resolve this conflict is ensuring that the minority is subordinate to the majority. For the first time, we study how the liquidated damages mechanism solves multi-principal conflict. This is another perspective that can be used to solve the conflict. Therefore, our paper expands the method of resolving the conflict and extends the theory of common agency; we first show the delegation process. Our research can be applied to various situations and provide a rational decision-making basis for participants. Full article

(This article belongs to the Topic Game Theory and Applications)

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24 pages, 5918 KiB  

Open AccessArticle

Evolutionary Game Analysis of Power Generation Groups Considering Energy Price Fluctuation

by Yu Jiang, Changyu Qian, Jie Yu, Luyao Zhou, Zheng Wang, Qian Chen, Yang Wang and Xiaole Ma

Algorithms 2022, 15(12), 456; https://doi.org/10.3390/a15120456 - 2 Dec 2022

Cited by 2 | Viewed by 1940

Abstract

As the double carbon target continues to be promoted and the installed capacity of gas-fired power generation gradually expands, whether and when gas-fired power generation should enter the market is a major concern for the industry. This paper analyzes the change in power [...] Read more.

As the double carbon target continues to be promoted and the installed capacity of gas-fired power generation gradually expands, whether and when gas-fired power generation should enter the market is a major concern for the industry. This paper analyzes the change in power generation cost and the characteristics of bidding behavior of the power generation group with the fluctuation of primary energy price to study the timing and role of gas power generation entering the market. The evolutionary game model for gas- and coal-fired power generation groups based on the influence of multiple factors takes into account factors such as generation costs, the number of power generation groups, generation capacity, supply, and demand. The equilibrium states of the power generation groups under various scenarios and the conditions that need to be satisfied for the equilibrium states are analyzed, and a method for determining the stable equilibrium point of the evolving market game is proposed. Examples use the actual price fluctuations of coal and natural gas as input data to validate the rationality of the paper’s model and the stable equilibrium approach. Full article

(This article belongs to the Topic Game Theory and Applications)

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20 pages, 469 KiB  

Open AccessArticle

Axioms of Decision Criteria for 3D Matrix Games and Their Applications

by Murat Özkaya, Burhaneddin İzgi and Matjaž Perc

Mathematics 2022, 10(23), 4524; https://doi.org/10.3390/math10234524 - 30 Nov 2022

Cited by 5 | Viewed by 4648

Abstract

In this paper, we define characteristic axioms for 3D matrix games and extend the definitions of the decision criteria under uncertainty to three dimensions in order to investigate the simultaneous effect of two different states on the decision process. We first redefine the [...] Read more.

In this paper, we define characteristic axioms for 3D matrix games and extend the definitions of the decision criteria under uncertainty to three dimensions in order to investigate the simultaneous effect of two different states on the decision process. We first redefine the Laplace, Wald, Hurwicz, and Savage criteria in 3D. We present a new definition depending on only the ∞-norm of the 3D payoff matrix for the Laplace criterion in 3D. Then, we demonstrate that the Laplace criterion in 3D explicitly satisfies all the proposed axioms, as well as the other three criteria. Moreover, we illustrate a fundamental example for a three-dimensional matrix with 3D figures and show the usage of each criterion in detail. In the second example, we model a decision process during the COVID-19 pandemic for South Korea to show the applicability of the 3D decision criteria using real data with two different states of nature for individuals’ actions for the quarantine. Additionally, we present an agricultural insurance problem and analyze the effects of the hailstorm and different speeds of wind on the harvest by the 3D criteria. To the best of our knowledge, this is the first study that brings 3D matrices in decision and game theories together. Full article

(This article belongs to the Topic Game Theory and Applications)

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8 pages, 428 KiB  

Open AccessArticle

Managerial Delegation and Conflicting Interest in Unionized Duopoly with Firm Heterogeneity

by Shih-Shen Chen, Po-Sheng Ko, Chien-Shu Tsai and Jen-Yao Lee

Mathematics 2022, 10(22), 4201; https://doi.org/10.3390/math10224201 - 10 Nov 2022

Cited by 3 | Viewed by 1502

Abstract

This paper utilized a three-stage dynamic game to analyze the conflicts of interest between stakeholders caused by firm heterogeneity. We show that the higher the degree of heterogeneity, the higher the sales delegation incentive given. The firm’s heterogeneity scale will cause industry profit, [...] Read more.

This paper utilized a three-stage dynamic game to analyze the conflicts of interest between stakeholders caused by firm heterogeneity. We show that the higher the degree of heterogeneity, the higher the sales delegation incentive given. The firm’s heterogeneity scale will cause industry profit, union utility, consumer surplus and manager bonus conflicts of interest. Furthermore, the intensity of conflict is lower between the industry and the union than between the industry and consumer and between the industry and manager if the degree of heterogeneity is relatively small. Full article

(This article belongs to the Topic Game Theory and Applications)

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20 pages, 378 KiB  

Open AccessArticle

Rational Play in Extensive-Form Games

by Giacomo Bonanno

Games 2022, 13(6), 72; https://doi.org/10.3390/g13060072 - 30 Oct 2022

Cited by 1 | Viewed by 3004

Abstract

We argue in favor of a departure from the equilibrium approach in game theory towards the less ambitious goal of describing only the actual behavior of rational players. The notions of Nash equilibrium and its refinements require a specification of the players’ choices [...] Read more.

We argue in favor of a departure from the equilibrium approach in game theory towards the less ambitious goal of describing only the actual behavior of rational players. The notions of Nash equilibrium and its refinements require a specification of the players’ choices and beliefs not only along the equilibrium play but also at counterfactual histories. We discuss an alternative—counterfactual-free—approach that focuses on choices and beliefs along the actual play, while being silent on choices and beliefs at unreached histories. Such an approach was introduced in an earlier paper that considered only perfect-information games. Here we extend the analysis to general extensive-form games (allowing for imperfect information) and put forward a behavioral notion of self-confirming play, which is close in spirit to the literature on self-confirming equilibrium. We also extend, to general extensive-form games, the characterization of rational play that is compatible with pure-strategy Nash equilibrium. Full article

(This article belongs to the Topic Game Theory and Applications)

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26 pages, 616 KiB  

Open AccessArticle

Construction of Equilibria in Strategic Stackelberg Games in Multi-Period Supply Chain Contracts

by Reza Azad Gholami, Leif Kristoffer Sandal and Jan Ubøe

Games 2022, 13(6), 70; https://doi.org/10.3390/g13060070 - 27 Oct 2022

Cited by 1 | Viewed by 2503

Abstract

Almost every supplier faces uncertain and time-varying demand. E-commerce and online shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research project is to provide an analytic tool for decentralized [...] Read more.

Almost every supplier faces uncertain and time-varying demand. E-commerce and online shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research project is to provide an analytic tool for decentralized supply channel members to devise optimal long-term (multi-period) supply, pricing, and timing strategies while catering to stochastic demand in a diverse set of market scenarios. Despite its ubiquity in potential applications, the time-dependent channel optimization problem in its general form has received limited attention in the literature due to its complexity and the highly nested structure of its ensuing equilibrium problems. However, there are many scenarios where a single-period channel optimization solution may turn out to be myopic as it does not consider the after-effects of current pricing on future demand. To remedy this typical shortcoming, using general memory functions, we include the strategic customers’ cognitive bias toward pricing history in the supply channel equilibrium problem. In the form of two constructive theorems, we provide explicit solution algorithms for the ensuing Nash–Stackelberg equilibrium problems. In particular, we prove that our recursive solution algorithm can find equilibria in the multi-periodic variation of many standard supply channel contracts such as wholesale, buyback, and revenue-sharing contracts. Full article

(This article belongs to the Topic Game Theory and Applications)

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17 pages, 490 KiB  

Open AccessArticle

Disassortative Mixing and Systemic Rational Behaviour: How System Rationality Is Influenced by Topology and Placement in Networked Systems

by Dharshana Kasthurirathna, Prasan Ratnayake and Mahendra Piraveenan

Mathematics 2022, 10(18), 3307; https://doi.org/10.3390/math10183307 - 12 Sep 2022

Viewed by 1690

Abstract

Interdependent decisionmaking of individuals in social systems can be modelled by games played on complex networks. Players in such systems have bounded rationality, which influences the computation of equilibrium solutions. It has been shown that the ‘system rationality’, which indicates the overall rationality [...] Read more.

Interdependent decisionmaking of individuals in social systems can be modelled by games played on complex networks. Players in such systems have bounded rationality, which influences the computation of equilibrium solutions. It has been shown that the ‘system rationality’, which indicates the overall rationality of a network of players, may play a key role in the emergence of scale-free or core-periphery topologies in real-world networks. In this work, we identify optimal topologies and mixing patterns of players which can maximise system rationality. Based on simulation results, we show that irrespective of the placement of nodes with higher rationality, it is the disassortative mixing of node rationality that helps to maximize system rationality in a population. In other words, the findings of this work indicate that the overall rationality of a population may improve when more players with non-similar individual rationality levels interact with each other. We identify particular topologies such as the core-periphery topology, which facilitates the optimisation of system rationality. The findings presented in this work may have useful interpretations and applications in socio-economic systems for maximizing the utility of interactions in a population of strategic players. Full article

(This article belongs to the Topic Game Theory and Applications)

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13 pages, 319 KiB  

Open AccessArticle

Sharpe-Ratio Portfolio in Controllable Markov Chains: Analytic and Algorithmic Approach for Second Order Cone Programming

by Lesly Lisset Ortiz-Cerezo, Alin Andrei Carsteanu and Julio Bernardo Clempner

Mathematics 2022, 10(18), 3221; https://doi.org/10.3390/math10183221 - 6 Sep 2022

Cited by 5 | Viewed by 2312

Abstract

The Sharpe ratio is a measure based on the theory of mean variance, it is the measure of the performance of a portfolio when the risk can be measured through the standard deviation. This paper suggests a Sharpe-ratio portfolio solution using a second [...] Read more.

The Sharpe ratio is a measure based on the theory of mean variance, it is the measure of the performance of a portfolio when the risk can be measured through the standard deviation. This paper suggests a Sharpe-ratio portfolio solution using a second order cone programming (SOCP). We use the penalty-regularized method to represent the nonlinear portfolio problem. We present a computationally tractable way to determining the Sharpe-ratio portfolio. A Markov chain structure is employed to represent the underlying asset price process. In order to determine the optimal portfolio in Markov chains, a new hybrid optimization programming method for SOCP is proposed. The suggested method’s efficiency and efficacy are demonstrated using a numerical example. Full article

(This article belongs to the Topic Game Theory and Applications)

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25 pages, 334 KiB  

Open AccessArticle

Copyright Enforcement in Content-Sharing Platforms

by Kameshwari Shankar

Games 2022, 13(5), 57; https://doi.org/10.3390/g13050057 - 25 Aug 2022

Viewed by 2195

Abstract

This paper analyzes the choice between quality improvements and copyright litigation by a proprietary seller who faces a competitive threat from a content-sharing platform. The platform operates like a “public good” with contributors who share content and free-riders who only consume content while [...] Read more.

This paper analyzes the choice between quality improvements and copyright litigation by a proprietary seller who faces a competitive threat from a content-sharing platform. The platform operates like a “public good” with contributors who share content and free-riders who only consume content while adding to congestion on the platform. When the proprietor can identify contributors in the platform with sufficient accuracy, a litigation strategy that targets contributors exacerbates free-riding behavior in the sharing platform and drives down platform quality. In contrast, investing in quality improvements for the copyrighted good does not affect contribution decisions on the platform, leading to a uniform decrease in the relative payoff for all users on the platform. The model presented in the paper shows that the proprietor finds litigation more profitable than quality improvements if she can target contributors accurately. Welfare analysis of the model shows that the proprietor has too high an incentive to invest in litigation and inefficiently low incentives for quality improvements of the copyrighted good. Full article

(This article belongs to the Topic Game Theory and Applications)

13 pages, 564 KiB  

Open AccessArticle

Media Trust: Official versus Commercial Outlets

by Xiaoli Guo

Games 2022, 13(4), 54; https://doi.org/10.3390/g13040054 - 3 Aug 2022

Cited by 2 | Viewed by 2941

Abstract

This paper presents a simple formal theoretical model to explain why citizens in authoritarian regimes trust the illiberal official media more than the commercial media. Media trust is defined as changes in the citizen’s belief based on good or bad news from the [...] Read more.

This paper presents a simple formal theoretical model to explain why citizens in authoritarian regimes trust the illiberal official media more than the commercial media. Media trust is defined as changes in the citizen’s belief based on good or bad news from the media. Using this definition, the model evaluates the independent and interaction effect of media bias, censorship, media quality, the citizen’s prior belief of the situation, and the citizen’s ideology on media trust. The findings reconcile some controversies in the literature, and, more importantly, reveal new and subtle explanations the literature did not identify and probably needs to pay attention to. Full article

(This article belongs to the Topic Game Theory and Applications)

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22 pages, 2752 KiB  

Open AccessArticle

Supply Chain Pricing Models Considering Risk Attitudes under Free-Riding Behavior

by Taiguang Gao, Kui Wang, Yali Mei, Shan He and Yanfang Wang

Mathematics 2022, 10(10), 1723; https://doi.org/10.3390/math10101723 - 18 May 2022

Cited by 3 | Viewed by 2414

Abstract

The free-riding behavior of companies that do not act will bring losses to companies that provide services. A market consists of two secondary supply chains: manufacturers and retailers. Each supply chain can choose to adopt promotional strategies to expand its market demand. This [...] Read more.

The free-riding behavior of companies that do not act will bring losses to companies that provide services. A market consists of two secondary supply chains: manufacturers and retailers. Each supply chain can choose to adopt promotional strategies to expand its market demand. This paper constructs the centralized decision-making in the supply chain and the Nash game competition model between supply chains and primarily studies the impact of risk aversion and the free-riding coefficient on supply chain pricing, promotion strategy selection, and expected utility. We show that the supply chain with high-risk aversion has relatively low pricing, but the demand and a total expected utility are high. We also identify that, on the premise of the same risk aversion degree of the two supply chains, when the free-riding coefficient between the chains is small and equal, the supply chain tends to implement the promotion strategy. When consumers have the same preference for the products of two retailers, the pricing of the free-riding supply chain increases with the increase in the free-riding coefficient, while the supply chain with a promotion strategy is the opposite. Based on the numerical results, we further give the optimal one-way free-riding coefficient when the two supply chains have the same degree of risk aversion; when there is a bidirectional free-riding behavior in the market, competition among supply chains gradually tends to the first two scenarios. Full article

(This article belongs to the Topic Game Theory and Applications)

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21 pages, 726 KiB  

Open AccessEditor’s ChoiceArticle

Sustainability of Intertwined Supply Networks: A Game-Theoretic Approach

by Olga Gorbaneva and Guennady Ougolnitsky

Games 2022, 13(3), 35; https://doi.org/10.3390/g13030035 - 28 Apr 2022

Cited by 7 | Viewed by 3322

Abstract

A formal game-theoretic model of an intertwined supply network, in full and simplified versions, is proposed. Conditions for the sustainable development of an active system are presented in general form and then specified to the class of intertwined supply networks. As an illustration, [...] Read more.

A formal game-theoretic model of an intertwined supply network, in full and simplified versions, is proposed. Conditions for the sustainable development of an active system are presented in general form and then specified to the class of intertwined supply networks. As an illustration, a concise example of the dynamic Cournot duopoly and a detailed example of the model of Social and Private Interests Coordination Engines (SPICE-model) for a marketing network are considered and analytically investigated and sustainability conditions are established. An important conclusion is that the sustainable development of the active system is possible only under the viability conditions satisfied simultaneously with coordinating the interests of all active agents of the system. Full article

(This article belongs to the Topic Game Theory and Applications)

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21 pages, 349 KiB  

Open AccessEditor’s ChoiceArticle

The Distributed Kolkata Paise Restaurant Game

by Kalliopi Kastampolidou, Christos Papalitsas and Theodore Andronikos

Games 2022, 13(3), 33; https://doi.org/10.3390/g13030033 - 20 Apr 2022

Cited by 5 | Viewed by 4011

Abstract

The Kolkata Paise Restaurant Problem is a challenging game in which n agents decide where to have lunch during their break. The game is not trivial because there are exactly n restaurants, and each restaurant can accommodate only one agent. We study this [...] Read more.

The Kolkata Paise Restaurant Problem is a challenging game in which n agents decide where to have lunch during their break. The game is not trivial because there are exactly n restaurants, and each restaurant can accommodate only one agent. We study this problem from a new angle and propose a novel strategy that results in greater utilization. Adopting a spatially distributed approach where the restaurants are uniformly distributed in the entire city area makes it possible for every agent to visit multiple restaurants. For each agent, the situation resembles that of the iconic traveling salesman, who must compute an optimal route through n cities. We rigorously prove probabilistic formulas that confirm the advantages of this policy and the increase in utilization. The derived equations generalize formulas that were previously known in the literature, which can be seen as special cases of our results. Full article

(This article belongs to the Topic Game Theory and Applications)

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19 pages, 309 KiB  

Open AccessArticle

A Family of Position Values for Directed Communication Situations

by Elena C. Gavilán, Conrado M. Manuel and René Van Den Brink

Mathematics 2022, 10(8), 1235; https://doi.org/10.3390/math10081235 - 9 Apr 2022

Viewed by 2006

Abstract

In this paper, we define a family of values for directed communication situations that are inspired by the position value. We use the concept of directed communication and related connectedness in directed graphs, under which a coalition of players in a game can [...] Read more.

In this paper, we define a family of values for directed communication situations that are inspired by the position value. We use the concept of directed communication and related connectedness in directed graphs, under which a coalition of players in a game can only cooperate if these players form a directed path in a directed communication graph. By defining an arc game, which assesses the worth of coalitions of (directed) arcs in generating worth, we allocate the Shapley value payoff of each arc over the nodes incident with this arc, where we allow the head and tail to obtain a different share in this arc payoff. However, the way that the arc payoff is shared over its head and tail is uniform over all arcs. We characterize these values by connection efficiency and a modification of the classical balanced link contributions property for undirected communication situations, discriminating between the roles of the nodes as head and tail. Full article

(This article belongs to the Topic Game Theory and Applications)

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16 pages, 1554 KiB  

Open AccessArticle

Impact of Third-Degree Price Discrimination on Welfare under the Asymmetric Price Game

by Zheng Zhang, Yingtong Wang, Qingchun Meng and Qiang Han

Mathematics 2022, 10(8), 1215; https://doi.org/10.3390/math10081215 - 7 Apr 2022

Cited by 3 | Viewed by 4781

Abstract

Whether third-degree price discrimination improves or damages social welfare has always been a hot topic for scholars of economics. At present, research studies on the impact of third-degree price discrimination on welfare have not been carried out under asymmetric price competition. To this [...] Read more.

Whether third-degree price discrimination improves or damages social welfare has always been a hot topic for scholars of economics. At present, research studies on the impact of third-degree price discrimination on welfare have not been carried out under asymmetric price competition. To this end, we studied this problem. In the research process, we divided consumers into two market segments by setting different travel costs based on the Hotelling model; at the same time, we considered three scenarios in which both firms engage in uniform pricing, both engage in price discrimination, and price discrimination vs. uniform pricing, and some intriguing findings and conclusions that differ from the previous studies were obtained through game analysis: (1) compared with two symmetric price games, the total output effect of each firm is unchanged, but the total social welfare is reduced, and as the size of the strong market increases, the reduction effect of total social welfare increases first and then decreases; (2) from local social welfare analysis, although the output of the firm adopting price discrimination remains unchanged, it can produce more producer surplus, consumer surplus and social welfare third-degree; (3) while the firm that uses uniform pricing is at a disadvantage in competition, the local social welfare created by it is decreased, and the reduction effect of social welfare will increase first and then decrease as the increase of the size of the strong market occurs. These conclusions reveal in an oligopoly market why enterprises always choose price discrimination and the government acquiesces in the existence of price discrimination. Full article

(This article belongs to the Topic Game Theory and Applications)

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23 pages, 3287 KiB  

Open AccessArticle

CEO Bias and Product Substitutability in Oligopoly Games

by Elizabeth Schroeder, Carol Horton Tremblay and Victor J. Tremblay

Games 2022, 13(2), 28; https://doi.org/10.3390/g13020028 - 31 Mar 2022

Cited by 1 | Viewed by 2969

Abstract

We investigate why a firm might purposefully hire a chief executive officer (CEO) who under- or over-estimates the degree of substitutability between competing products. This counterintuitive result arises in imperfect competition because CEO bias can affect rival behavior and the intensity of competition. [...] Read more.

We investigate why a firm might purposefully hire a chief executive officer (CEO) who under- or over-estimates the degree of substitutability between competing products. This counterintuitive result arises in imperfect competition because CEO bias can affect rival behavior and the intensity of competition. We lay out the conditions under which it is profitable for owners to hire biased managers. Our work shows that a universal policy that effectively eliminates such biases need not improve social welfare. Full article

(This article belongs to the Topic Game Theory and Applications)

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18 pages, 625 KiB  

Open AccessArticle

Auction and Classification of Smart Contracts

by Damián-Emilio Gibaja-Romero and Rosa-María Cantón-Croda

Mathematics 2022, 10(7), 1033; https://doi.org/10.3390/math10071033 - 24 Mar 2022

Cited by 2 | Viewed by 2606

Abstract

The execution of smart contracts (SCs) relies on consensus algorithms that validate the miner who executes the contract and gets a fee to cover her expenditure. In this sense, miners are strategic agents who may focus on executing those contracts with the largest [...] Read more.

The execution of smart contracts (SCs) relies on consensus algorithms that validate the miner who executes the contract and gets a fee to cover her expenditure. In this sense, miners are strategic agents who may focus on executing those contracts with the largest fee, to the detriment of other SCs’ execution times, which also harms the blockchain’s reputation. This paper analyzes the impact of miners’ competition on SCs’ execution times in a public blockchain. First, we explain that the Proof-of-Work mechanism casts similarities with a time auction, where the one who first adds blocks is the one who executes the contract and gets the fee. At equilibrium, costs negatively affect execution times, while the opposite holds concerning fees. However, this result does not capture the competition for other contracts; hence, we apply the Naïve Bayes method to classify SCs by considering a simulated database that comprises miners’ competition for several contracts. We observe that simultaneous competition generates patterns that differ from the ones expected by the auction solution. For example, miners’ valuation does not accelerate contracts’ execution, and high-cost smart contracts do not necessarily execute at last places. Full article

(This article belongs to the Topic Game Theory and Applications)

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21 pages, 661 KiB  

Open AccessArticle

Stochastic Game Analysis of Cooperation and Selfishness in a Random Access Mechanism

by Ahmed Boujnoui, Abdellah Zaaloul, Luis Orozco-Barbosa and Abdelkrim Haqiq

Mathematics 2022, 10(5), 694; https://doi.org/10.3390/math10050694 - 23 Feb 2022

Cited by 3 | Viewed by 2414

Abstract

This paper introduces a general stochastic game analysis of a network scenario consisting of a mix of cooperative and non-cooperative players (i.e., users) under incomplete game information. Users access a shared channel using the Slotted ALOHA mechanism combined with ZigZag Decoding (SAZD). Cooperative [...] Read more.

This paper introduces a general stochastic game analysis of a network scenario consisting of a mix of cooperative and non-cooperative players (i.e., users) under incomplete game information. Users access a shared channel using the Slotted ALOHA mechanism combined with ZigZag Decoding (SAZD). Cooperative players seek to optimize the global utility of the system (e.g., throughput, delay, loss rate) regardless of their individual interests, whereas non-cooperative players act selfishly and optimize their own benefits irrespective of the impact of this behavior on others and on the entire network system. The game equilibrium is characterized by the social optimum and the Nash equilibrium, where the former is adopted by cooperative players and the latter is the equilibrium strategy of non-cooperative players. We undertake a comparative study across two game scenarios with different levels of cooperation and selfishness. Our results generally show that the information possessed by a player can determine the outcome. Furthermore, our findings show that the network performance is strongly influenced by selfish behavior, which can lead to a significant disruption of the entire system. Finally, we show a possible scenario in which the network could greatly benefit from this selfish behavior thanks to the ZigZag scheme. Full article

(This article belongs to the Topic Game Theory and Applications)

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