Optimization models with economic and game theoretic applications

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Nowadays, games exist everywhere in people's daily life, and game theory methods should not be just formulas and words in books, but also brought into people's daily life, helping people to solve many practical problems in life. This paper selects the most common problem in the life of postgraduate students - the choice of thesis direction between postgraduate students and their supervisors, takes Nash equilibrium as the theoretical support point, analyses the "prisoner's dilemma" model in game theory, combines with the payment matrix, and finds the solution to the problem. The solution to the problem is the application of game theory in daily life, which demonstrates the close connection between games and life.

In many respects, water resources allocation problems have fuzzy characteristics owing to uncertainty and imprecision not only as numerical data but also as linguistic data, in addition to the political nature of resource allocation. All classical techniques require numerical data and cannot treat linguistic data, but fuzzy inference systems (FIS) can deal with both types of data. Hence, it is suitable to reflect the dynamic nature of country benefits, reflective variations in the main drainage and subdrainage basin flows, and various system parameters in search of a coalition among a few riparian countries. The size of core, which is generated from a series of linear programming (LP) optimization models and game theory concepts, shows the potential extra benefit advantage of being in grand coalition to all parties, but it does not provide a sufficient condition to assemble a robust coalition unless an agreeable allocation scheme or principle is provided. In this respect, there is a fuzzy link between being in the grand coalition and percentage share received from a core. Hence, a proper FIS is proposed, and the necessary steps are developed with the Shapley value and the core as game theory methods, which provide a methodological base in the evaluation of possible allocation schemes among the parties. The application of the methodology is presented to search for coalition possibilities among the riparian countries: Turkey, Syria, and Iraq. Basic results are generated over the application of the Inter‐Temporal Euphrates and Tigris River Basin Model, which is an optimization model for the allocation of scarce water resources considering agricultural and urban uses, energy generation, and conveyance costs in the Euphrates‐Tigris basin.

The article deals with the application of game theory models in jurisprudence. Although the problem of the application of interdisciplinary methods in law is currently very relevant, in modern Russian legal science, the theory of games has not received proper distribution. In the domestic scientific literature, there are mainly prerequisites for the use of a game-theoretic approach in law, but there is almost no further development of the idea of applying game theory in law. The author sets the task to identify some game-theoretic models that could be useful for jurisprudence. The article evaluates three legal game-theoretic models. These models were divided by the level of subjects participating in legal relations, which is demonstrated by examples. The study also searches for judicial practice in which game-theoretic elements can be found. As a result of the application of game-theoretic models, an analysis of legal relations was carried out, which indicates how the law can interfere in legal relations for more effective legal regulation. It is proved that game theory models are useful for jurisprudence, and the use of a game-theoretic approach in law needs to be developed.

Discrete time spatial models arising in genetics, evolutionary game theory, and branching processes.

This paper develops two models to investigate the impact of a tariff on logistics strategies in an international e-commerce trade, where the methods of game theory and agent-based model are utilized. We consider a foreign supplier and a domestic e-tailer. There are two logistics strategies: the supplier undertakes the logistics and the e-tailer shoulders the logistics. First, two strategies are compared under the game theory model. Then, we capture the uncertainties of market demand and tariff. An agent-based model is adopted to further study how the tariff affects the supply chain’s decisions and strategies. Some meaningful results are obtained. (i) The supplier should provide the logistics service when market demand and tariff are certain. (ii) Under demand uncertainty, the supplier and the e-tailer can reach an agreement on logistics strategies when the tariff is small. (iii) When tariff uncertainty is moderate, two players both abandon the logistics intention..

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The information based on the tripartite (truth, indeterminacy, and falsity) can be described by single-valued neutrosophic numbers, but the linguistic information based on these tripartite cannot be represented by single-valued neutrosophic numbers. To overcome this obstacle, linguistic single-valued neutrosophic numbers are characterized independently by the truth, indeterminacy, and falsity linguistic variables. In this paper, some new operations are introduced to increase the richness of linguistic fusion based on the linguistic single-valued neutrosophic approach. The Hamming distance-based formula is proposed to measure the distance between two linguistic single-valued neutrosophic numbers. Afterwards, we initiate the theory of linguistic single-valued neutrosophic soft (LSVNS) set by combining linguistic single-valued neutrosophic set and soft set. Meanwhile, the different computational functions and desirable properties of LSVNS sets are studied. Furthermore, we construct the framework of LSVNS technique for order preference by similarity to ideal solution (TOPSIS) and then present a game theory model based on this framework. Finally, we give an outstanding example to validate the practicality and effectiveness of the proposed LSVNS TOPSIS-based game theory model.

a national defense policy, and in particular in their relation to deterrence. In the course of the last twenty years there has been a considerable growth in methods and theories concerning different aspects of human behavior. In particular, in situations involving conscious choice under conditions of possible conflict or cooperation there has been a development in political science, mathematical economics, programming, psychology, simulation, gaming, and game theory. For several years an expectation was built up that game-theoretical models would make an immediate operational contribution to the applied art and hoped-for science of weapons control. The diplomat, the general, and the social scientist, when confronted with the ill-defined and the uncontrollable, have often hoped for a witchmedicine to solve their problems. A common modern formula for the powerful witch medicine contains a game-theoretic model and a large digital computer. Unfortunately, neither the growth of methodology nor technology by itself can solve problems which require a deep substantive knowledge. This does not mean that the new

Game Theory is branch of applied mathematics that provides tools for analyzing situations, which has better solved the operability analysis of competition and other problems, and has become a research field in economics. Many kinds of behaviors and phenomena around us can be summarized by game theory. This paper mainly introduces the concept of game theory, the application classification of game theory, the classical model of game theory and the application of game theory in life.

Diversion hypothesis has ended up a valuable way to portray and make strides complicated connections in numerous zones, such as savvy framework vitality administration. When it comes to savvy lattice operations, the truth that vitality generation, exchange, and utilize are all energetic and separated makes huge issues that are difficult to fathom with standard controlled strategies. This outline looks at how amusement hypothesis can be utilized to assist individuals make better decisions and make the leading utilize of assets in savvy framework settings. The most objective is to figure out how game-theoretic models can offer assistance with productive vitality management by looking at how diverse parties, like clients, providers, and lattice administrators, will act in numerous circumstances. Regularly, these bunches have objectives that are at chances with each other, like minimizing costs, making as much cash as possible, and ensuring the environment. Amusement hypothesis lets us see at these trades as in case they were arranged recreations, with each individual attempting to get the foremost out of the diversion by altering their claim choices and the activities of others. Key thoughts from diversion hypothesis, like Nash harmony, agreeable and non-cooperative diversions, and component plan, are utilized to come up with keen framework operations procedures that are both reasonable and proficient. Nash balance could be a key thought for a arrangement where no individual can pick up by changing their arrange on their possess. This provides security in independent decision-making. In addition, the abstract talks about a number of case studies and uses where game theory has been used successfully in smart grids. Some of these are demand response programs, energy trade markets, and making the best use of integrating green energy. By making these events into games, parties can plan for and deal with problems like grid instability, price changes, and traffic jams. The outline also talks about problems that are still being researched and where the field might go in the future. These include making game-theoretic models work on large-scale smart grid networks, using real-time data analytics to help people make better decisions, and using machine learning to make predictions more accurate.

How to make correct business decisions has become a hot issue that entrepreneurs are concerned about. Some researchers have found that game theory greatly impacts business decisions. However, there is still a lack of a unified explanation of the formation mechanism behind using game theory to make correct business decisions. Therefore, this article explores the use of game theory to make correct business decisions by collecting data on business competition, organizing the data into a benefit matrix, and comparing to conclude, through which the benefits of business cooperation and business competition can be demonstrated. Through research, it is found that game theory plays an important role in business decision-making, which makes a significant difference in planning the future development path of the enterprise. By using game theory models such as the Prisoner’s Dilemma and boxed pigs, entrepreneurs can make optimal business decisions. Through an in-depth understanding of the relevant knowledge of game theory, entrepreneurs can know the timing and maximum benefits of business cooperation and competition, which provides important tips for enterprise reform and development in the new era.

Objective: economic and legal description, formal justification and construction of models of the balanced economic, legal and social macrosystems in order to determine effective strategic decisions under uncertainty.Methods: the theoretical and methodological basis of the study is the synthesis of the provisions and principles of game and management theories, economic and mathematical modeling and the game-theoretical models of decision-making in complex systems developed on their basis, as well as theoretical and methodological approaches of system analysis, economics, sociology, and law.Results: the balance of economic, legal and social systems is determined by the target orientation to the growth of the population’s well-being. The existing mechanisms for achieving this balance do not take into account the interests of all participants of the systems. The paper presents a structural analysis of the interaction and mutual influence of economic, legal and social macrosystems (a complex metasystem); the necessity of transforming the existing approaches to their regulation is shown. The problem of ensuring the systems’ balancing is largely related to the conflict of interests of the parties. Therefore, traditional methods of modeling decision-making processes do not reflect the real socio-economic processes. This problem was solved through game-theory models that contribute to the implementation of the constitutionally established norms which define Russia as a social state. When making strategic decisions in the social sphere, it is proposed to use the concept of the Golden rule of morality as the main economic doctrine, instead of the currently used neoliberal approach, based, among other things, on the concept of Nash equilibrium. The equilibrium models of the complex metasystem by Nash and Berge were formalized, constructed and compared.Scientific novelty: in contrast to the Nash equilibrium (principles of rationality) - the traditional approach used in the construction of equilibrium models, - the paper offers a theoretical justification of the development and construction of equilibrium models and balance sheet equilibrium of economic, legal and social macrosystems by Berge, as well as a formalization of effective strategic decisions and their respective risks.A distinctive feature of the constructed macromodels is the use of the philosophical and moral concept of the Golden rule (the mathematical basis is the balance by Berge) as an economic doctrine for strategic decision-making under uncertainty, and the construction of the so-called guaranteed optimal solutions by Pareto (effective), based, among other things, on the concept of the pair “social guarantee - life risk”. If, in real conditions, one of the macrosystems is economic and is a “generator” of uncertainties, a guaranteed solution is formalized, optimal by Slater (weakly effective).Practical significance: the developed methodology for building the system equilibrium of economic, legal and social macro-systems enables to make decisions socially significant for the population that adequately take into account the peculiarities of the modern socio-economic macro-systems, such as nonstationarity, dysfunctionality, incomplete information, inconsistency, conflict, alternatives, multicriterial character, and risk; and to develop assisting intellectual systems of supporting decision-making based on mathematical models built using the game-theory approach.

The article’s aims to reveal the application of game theory in terms of more effective management of organizational changes. To achieve the main goal, two problems immediately arise: Why is the context of organizational change suitable for game-theoretic analysis? What are the possible and significant applications of game theory in change management? This study is not devoted to any specific case of change. It does not contain an analysis of one specific problem. The article presents possible and significant theoretical applications of game theory to the problems of organizational change, not an in-depth modelling of one problem. For this reason, several situations were identified in which the application of game theory is appropriate, and games were modelled for those situations. The basis for game modelling was a survey among the management and employees of Tele Performance Armenia. Thus, problem areas of organizational changes were identified as an analysis method and mechanisms for applying game theory and detailed problem analysis were used. Relevant games were proposed, and their solutions or equilibrium points were discussed. The method used will automatically show the practical application of game theory in complex situations of change implementation. As a result of the analysis, it was concluded that possible main functions of game theory are equilibrium analysis, strategy formulation, providing abstract advice, as well as interpretation and description of complex situations for change implementation as an analytical tool.