Solution Of Game Research Articles

Pareto efficiency as alternative to Nash equilibrium in competitive discrete location under delivered pricing

We address the facility location problem for firms that sell an homogeneous product and compete on delivered prices. If the firms set equilibrium prices at each market, the problem can be seen as a location game for which there exists a Nash equilibrium if demand is inelastic. However, this equilibrium may be Pareto-inefficient and the firms could decide to collude if they can guarantee themselves higher payoffs than those prescribed by the equilibrium. The aim of this paper is to study the joint profit maximization problem to obtain a collusive solution of the location game (Pareto-efficient) and determine if such a solution is also a Nash equilibrium. We develop Integer Linear Programming models to find Pareto-efficient solutions for multiple and single facility location. Nash equilibria are obtained by the best response procedure. An empirical investigation is performed to compare the joint profit of the firms and the profit of each one of the firms, got through the Pareto-efficient locations, with those got through the Nash equilibrium.

Potentials and solutions of cooperative games with a fixed player set

Potentials and solutions of cooperative games with a fixed player set

On the structure of core solutions of discontinuous general cooperative games

On the structure of core solutions of discontinuous general cooperative games

Distributed Adaptive Nash Equilibrium Solution for Differential Graphical Games.

This article investigates differential graphical games for linear multiagent systems with a leader on fixed communication graphs. The objective is to make each agent synchronize to the leader and, meanwhile, optimize a performance index, which depends on the control policies of its own and its neighbors. To this end, a distributed adaptive Nash equilibrium solution is proposed for the differential graphical games. This solution, in contrast to the existing ones, is not only Nash but also fully distributed in the sense that each agent only uses local information of its own and its immediate neighbors without using any global information of the communication graph. Moreover, the asymptotic stability and global Nash equilibrium properties are analyzed for the proposed distributed adaptive Nash equilibrium solution. As an illustrative example, the differential graphical game solution is applied to the microgrid secondary control problem to achieve fully distributed voltage synchronization with optimized performance.

Players’ dummification and the dummified egalitarian non-separable contribution value

This paper introduces a new solution for cooperative games, called dummified egalitarian non-separable contribution (DENSC) value. This value is obtained by minimizing the variance of so-called dummified grand complaints of coalitions, and is characterized in term of the axioms on players’ dummification.

Machine learning driven extended matrix norm method for the solution of large-scale zero-sum matrix games

Machine learning driven extended matrix norm method for the solution of large-scale zero-sum matrix games

Игрофикация учебно-воспитательного процесса вузов

Training of highly qualified specialists in modern conditions requires gamification of the educational process itself in higher education. The article is aimed at substantiating the need to expand the field of game practice in the system of higher education by including gamification of the educational process of universities and outlining the conceptual foundations of the author’s innovative method of organizing the educational and educational process in the system of higher education VIRTUOZ (‘Variable Game Solution of Difficult Educational Tasks’). The article provides a detailed review of the subject field of scientific publications of domestic and foreign researchers on games and game practices in higher education, which showed that they comprehensively consider gamification in higher education, with attention to various types of games. However, the problem of gamification of the educational and upbringing process itself, the tasks solved by it before the author, no one in the Russian Federation and abroad has investigated and implemented in practice. The author substantiates that it is advisable to gamify the organization of educational activities of the university in order to make this process meet the requirements of the transformation of national education, deeper and more justified. The VIRTUOZ method is designed to help in the effective formation of competencies in solving the corresponding specific task: writing a WRC, undergoing practical training and others. The uniqueness of the project lies, first of all, in the fact that it involves the comprehensive interaction of all participants in the educational process; is implemented on the basis of the results of a sociological survey on a particular problem to identify the most difficult tasks; simulates the game situation, based on the specifics of the university, the subject and other factors; ensures effectiveness for all participants in the educational process. The VIRTUOZ project makes extensive use of end-to-end technologies and digital tools. The VIRTUOZ method opens the way for the development and implementation of other innovative game methods for organizing the educational process in higher education.

Cooperative Games Based on Coalition Functions in Biform Games

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.

Strategic Resource Pricing and Allocation in a 5G Network Slicing Stackelberg Game

We consider a marketplace in the context of 5G network slicing, where Application Service Providers (ASP), <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.,</i> slice tenants, providing heterogeneous services, are in competition for the access to the virtualized network resource owned by a Network Slice Provider (NSP), who relies on network slicing. We model the interactions between the end users (followers) and the ASPs (leaders) as a Stackelberg game. We prove that the competition between the ASPs results in a multi-resource Tullock rent-seeking game. To determine resource pricing and allocation, we devise two innovative market mechanisms. First, we assume that the ASPs are pre-assigned with fixed shares (budgets) of infrastructure, and rely on a trading post mechanism to allocate the resource. Under this mechanism, the ASPs can redistribute their budgets in bids and customise their allocations to maximize their profits. In case a single resource is considered, we prove that the ASPs’ coupled decision problems give rise to a unique Nash equilibrium. Second, when ASPs have no bound on their budget, we formulate the problem as a pricing game with coupling constraints capturing the shared resource finite capacities, and derive the market prices as the duals of the coupling constraints. In addition, we prove that the pricing game admits a unique variational equilibrium. We implement two online learning algorithms to compute solutions of the market mechanisms. A third fully distributed algorithm based on a proximal method is proposed to compute the Variational equilibrium solution of the pricing game. Finally, we run numerical simulations to analyse the market mechanism’s economic properties and the convergence rates of the algorithms.

Social Media Manipulation Awareness through Deep Learning based Disinformation Generation

As a digital environment introduced for establishing and enhancing human communication through different social networks and channels, social media continued to develop and spread at an incredible rate making it difficult to find or imagine a concept, technology, or business that does not have or plan to have its social media representation and space. Concurrently, social media became a playground and even a battlefield where different ideas carrying out diverse validity degrees are spread for reaching their target audiences generated by clear and trustable well-known, uncertain, or even evil aimed entities. In the stride carried out for preventing, containing, and limiting the effects of social manipulation of the last two types of entities, proper/effective security awareness is critical and mandatory in the first place. On this behalf, several strategies, policies, methods, and technologies were proposed by research and practitioner communities, but such initiatives take mostly a defender perspective, and this is not enough in cyberspace where the offender is in advantage in attack. Therefore, this research aims to produce social media manipulation security awareness taking the offender stance by generating and analysing disinformation tweets using deep learning. To reach this goal, a Design Science Research methodology is followed in a Data Science approach, and the results obtained are analysed and positioned in the ongoing discourses showing the effectiveness of such approach and its role in building future social media manipulation detection solutions. This research also intends to contribute to the design of further transparent and responsible modelling and gaming solutions for building/enhancing social manipulation awareness and the definition of realistic cyber/information operations scenarios dedicated/engaging large multi-domain (non)expert audiences.

Properties of Solutions for Games on Union-Closed Systems

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions to every TU-game. In the literature, various models of games with restricted cooperation can be found where, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider games on a union-closed system where the set of feasible coalitions is closed under the union, i.e., for any two feasible coalitions also, their union is feasible. Properties of solutions (the core, the nucleolus, and the prekernel) are discussed for games on a union-closed system.

Mini-Map Design Features as a Navigation Aid in the Virtual Geographical Space Based on Video Games

The main objective of this study is to identify features of mini-map design as a navigational aid in the virtual geographical space in 100 popular video games for a computer platform. The following research methods were used: visual comparative analysis, classification and selection of cartographic material, comparison of specific parameters for selected features of design elements, and application of cartographic design rules and popularity of design solutions in video games. The study revealed eight features of mini-map design and their popular parameters and attributes in video games, with only one game meeting all conditions of popularity: projection: orthographic; centring: player-centred; base layers: artificial; shape: circle; orientation: camera view; position: bottom left; proportions: 2.1–3%; additional navigational element: north arrow. The key attributes of the mini-map’s features were captured, which, when considered separately, complementarily and potentially holistically, confirm the possibility of designing the mini-map according to traditional cartographic design principles. The identified parameters of the mini-map can be useful not only in the design of the game cartography interface, but also for other geomedia products.

A new biform game-based investment incentive mechanism for eco-efficient innovation in supply chain

In supply chain, when a visionary focal firm makes direct investment in his partners’ upfront cost of eco-efficient innovation, he would want more innovation efforts without sacrificing too many self-interests. To this end, we use a new biform-game model to develop an investment incentive mechanism for eco-efficient innovation in a supply chain consisting of two competing manufactures who are accountable for their respective eco-efficient innovations and a supplier who provides them with investments. Our proposed biform-game model can be regarded as a nested combination of noncooperative and cooperative games: In the noncooperative part, we construct a noncooperative game between the two manufacturers under their profit maximizing strategies, defining the competitive environment in the cooperative part. For three players in the cooperative part, we use Minimax and Maximin principles to construct their cooperative game of the investment cooperation strategy, which is proven to be convex. Subsequently, Shapley value is employed to derive the solution (profits) of the cooperative game, which is used to deduce the pay-off functions of the noncooperative part, thereby obtaining the optimal profit-maximizing strategies and investment cooperation strategies of the biform game. Next, we conduct analytical and numerical studies to verify the validity of our developed model by comparing with the model without applying the biform coordination mechanism.

Assessment Method for Demand Side User Response Potential based on Game Theory and Information Value

An accurate assessment of user demand response potential is helpful for power companies or load aggregators to rationally call demand-side resources, improve the implementation effect of demand response, and reduce the peak-valley load difference of power systems. This paper proposes a new approach based on game theory and information value to evaluate the response potential of demand-side users. Firstly, the evaluation index system of user response potential is established based on user history behaviors, user basic information, aggregator’s incentive to users, and user’s information value. Secondly, based on game theory, the total of subjective and objective weights is integrated, and the game solution of evaluation index weight is obtained. Finally, the user potential assessment results are quantified based on the fuzzy optimization set pair analysis theory to achieve an accurate online assessment of the demand-side user response potential.

Rich Extensions of the Core and the Equal Split Off Set

This paper studies extensions of the core and the equal split off set (ESOS) for TU games, and also subsolutions of the extensions in order to derive some new egalitarian solutions for TU games. Stability of the allocations is weakened such that an allocation [Formula: see text] can be blocked only by rich coalitions which together with a player will contain all players having payoffs not less than him. In accordance with such a definition of blocking, two new solutions — the rich core and the egalitarian rich core — are defined and characterized by means of weakening of axioms characterizing the ESOS on the class of all TU games [Dietzenbacher, B. and Yanovskaya, E. [2021] Consistency of the equal spit-off set, Int. J. Game Theory 50(1), 1–22]. Two subsolutions of the egalitarian rich core — the set of Lorenz undominated allocations and the set of allocations that lexicographically minimize maximal payoffs of players (Lmax solution) are characterized. The tight upper boundary of the number of allocations in the ESOS and in the egalitarian rich core is found.

Attack against layered defense

The ''attack-defense'' model is considered, in which the defense party at each point of defense has several lines and uses the target allocation of its forces. The problem of minimizing the mean quantity of attack forces breaking through the defense lines is solved in explicit formulae. Algorithm of finding a solution of the zero-sum damage game is developed.

Imperfect vaccine can yield multiple Nash equilibria in vaccination games

As infectious diseases continue to threaten communities across the globe, people are faced with a choice to vaccinate, or not. Many factors influence this decision, such as the cost of the disease, the chance of contracting the disease, the population vaccination coverage, and the efficacy of the vaccine. While the vaccination games in which individuals decide whether to vaccinate or not based on their own interests are gaining in popularity in recent years, the vaccine imperfection has been an overlooked aspect so far. In this paper we investigate the effects of an imperfect vaccine on the outcomes of a vaccination game. We use a simple SIR compartmental model for the underlying model of disease transmission. We model the vaccine imperfection by adding vaccination at birth and maintain a possibility for the vaccinated individual to become infected. We derive explicit conditions for the existence of different Nash equilibria, the solutions of the vaccination game. The outcomes of the game depend on the complex interplay between disease transmission dynamics (the basic reproduction number), the relative cost of the infection, and the vaccine efficacy. We show that for diseases with relatively low basic reproduction numbers (smaller than about 2.62), there is a little difference between outcomes for perfect or imperfect vaccines and thus the simpler models assuming perfect vaccines are good enough. However, when the basic reproduction number is above 2.62, then, unlike in the case of a perfect vaccine, there can be multiple equilibria. Moreover, unless there is a mandatory vaccination policy in place that would push the vaccination coverage above the value of unstable Nash equilibrium, the population could eventually slip to the “do not vaccinate” state. Thus, for diseases that have relatively high basic reproduction numbers, the potential for the vaccine not being perfect should be explicitly considered in the models.

An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem

This paper presents an approach for the solution of a zero-sum differential game associated with a nonlinear state-feedback H∞ control problem. Instead of using the approximation methods for solving the corresponding Hamilton–Jacobi–Isaacs (HJI) partial differential equation, we propose an algorithm that calculates the explicit inputs to the dynamic system by directly performing minimization with simultaneous maximization of the same objective function. In order to achieve numerical robustness and stability, the proposed algorithm uses: quasi-Newton method, conjugate gradient method, line search method with Wolfe conditions, Adams approximation method for time discretization and complex-step calculation of derivatives. The algorithm is evaluated in computer simulations on examples of first- and second-order nonlinear systems with analytical solutions of H∞ control problem.

GPI-Based design for partially unknown nonlinear two-player zero-sum games

This article focuses on obtaining the solution of two-player zero-sum games (ZSGs) where the saddle point may not exist. From the standpoints of the upper performance index function (PIF) and lower PIF separately, we seek the solution of two-player differential ZSGs without assuming the strict existence of saddle point. To achieve the objective, we apply the generalized policy iteration (GPI) technique to design the controller. With neural network approximators, the system trajectory data are used to update the approximation of the PIFs. It is established that the upper (lower) PIF sequence is convergent along the iteration axis under the GPI scheme. When the two function sequences converge to equal values, the saddle point is attained, and vice versa. Numerical simulation results conformed to the suitability of the designed algorithm.

On the solution of games with arbitrary payoffs: An application to an over‐the‐counter financial market

AbstractThis paper defines a variety of game theoretic solution concepts in the language of soft set theory. We begin by defining the Nash equilibrium in pure strategies. We assume that the gains of the players are totally ordered and non‐desirable alternatives are absent. Moreover, we introduce the notions of strong and semi‐strong utility. These two completely new notions, serve as a mechanism for converting non‐ordered gains into totally ordered ones. We define the Nash equilibrium in mixed strategies in a general framework by introducing the notion of an extended game and strategy space. We finally define the Nash solution to cooperative bargaining games within the framework of soft set theory, illustrate a practical application to an over‐the‐counter financial market, and provide a detailed numerical example.