Mathematical Game Theory Research Articles

The application of operation research in the design of on-site construction organization

This article explores the integration of Operations Research (OR) principles in the design and management of on-site construction organizations. The first section introduces Operations Research as a multidisciplinary field that employs mathematical modelling, statistical analysis, and optimization techniques to enhance decision-making processes across various sectors. Key aspects such as mathematical modelling, optimization, decision analysis, simulation, queueing theory, linear programming, and game theory are highlighted. The second section focuses on the design of on-site construction organizations, emphasizing the structure and organization of resources, personnel, and processes essential for efficient project execution. Various key elements, including project management, site personnel, project support teams, engineering and design teams, health and safety personnel, procurement and supply chain, communication and coordination, equipment and maintenance, and environmental compliance, are discussed. The third section delves into the application of Operations Research techniques in the design and management of on-site construction organizations. It outlines how OR principles can be employed for resource allocation and optimization, project scheduling and planning, inventory management, equipment utilization, project costing and budgeting, risk management, supply chain management, human resource management, facility layout and design, and the development of decision support systems. The conclusion highlights that the strategic application of Operations Research methodologies contributes to enhanced efficiency, optimized resources, and improved decision-making throughout the construction project lifecycle. The integration of OR principles not only enhance the overall effectiveness of on-site construction organizations but also leads to cost savings, timely project completion, and improved project outcomes. As construction projects continue to grow in scale and complexity, the systematic and analytical approach provided by Operations Research becomes increasingly valuable in addressing the intricate challenges faced by construction stakeholders.

Mathematical Game Theory at St. Petersburg State University

The paper is dedicated to the 300th anniversary of St. Petersburg State University. Creation of the school of mathematical game theory at St. Petersburg State University is associated with Nikolai Nikolaevich Vorobyov. The school has an interesting history described in the paper. More than 50 scientists working in the leading Russian and international scientific centers all over the world in the field of differential, dynamic, and cooperative games were the students of this school.

STRATEGIC TRANSFORMATIONS: INDIA'S PURSUIT OF COUNTERFORCE TARGETING AND REGIONAL STABILITY

In the intricate web of South Asia's security dynamics, India and Pakistan's relationship holds the key to equilibrium. Geographical proximity demands swift responses, prompting India's strategic shift towards Counterforce targeting. Official declarations and military posturing attest to India's resolute commitment to recalibrate its deterrence doctrine. This study critically examines the origins of India's Counterforce targeting strategy, drawing from existing literature and employing theoretical frameworks, including posture optimization, escalation ladder, superiority-brinkmanship, mathematical game theory, rational choice theory, and nuclear deterrence. These models collectively contribute to understanding the implications of India's pursuit of nuclear superiority for coercive diplomacy with Pakistan. Beyond enriching the understanding of South Asia's security, this research unravels the interplay between evolving nuclear strategies, the fluid dynamics of deterrence, and nuanced geopolitical ambitions. By deciphering India's counterforce targeting approach, this study fosters a nuanced discourse on South Asian strategic stability, offering insight into the pivotal role of nuclear deterrence in shaping the region. Bibliography Entry Ashraf, Mubeen and Syed Saif ul Haq. 2023. "Strategic Transformations: India's Pursuit of Counterforce Targeting and Regional Stability." Margalla Papers 27 (2): 14-26.

Методы поддержки принятия решений в оперативном управлении при чрезвычайных ситуациях: обзор исследований

The article examines the problem of operational management in emergencies. At the content level, an analysis of strategic, tactical and operational management in emergency situations was carried out, and their intended purpose was determined. The content of operational management decisions at different stages of emergency situations has been studied. Limitations that directly affect operational management in emergencies have been identified. 
 A systematic analysis of scientific research is carried out and examples are given in the context of work related to operational management in emergencies regarding the stages of emergency development. Research highlights include articles in the fields of mathematical modeling, simulation modeling, game theory and decision making, artificial intelligence and knowledge management. The main promising directions for further research have been identified.

Preface to the Special Issue “Fixed Point Theory and Dynamical Systems with Applications”

Since the celebrated Brouwer’s fixed point theorem and Banach contraction principle were established, the rapid growth of fixed point theory and its applications have led to a number of scholarly essays studying the importance of its promotion and application in nonlinear analysis, applied mathematical analysis, economics, game theory, integral and differential equations and inclusions, dynamic systems theory, signal and image processing, etc [...]

Model of interaction between the government and business towards legalization of unorganized imports

Ukraine’s economy quickly integrated into the system of shadow financial flows and used standard tools to manipulate export and import prices and financial instruments. In terms of cumulative outflows of shadow capital, Ukraine is among the top twenty countries. The research relevance is predefined by the main directions of legalization of economic processes, including in the segment of shadow imports, which involve the formation of optimal institutional strategies for the behaviour of social agents (government and business). The research aims to select the Government’s strategy for legalizing unorganized imports, which will allow the establishment of effective interaction between social agents on mutually beneficial terms. Research methods include mathematical analysis and game theory, used to build mathematical models, which reveal the intrinsic rationality of individual interactions, aggregating a set of social situations into several options and reducing the uncertainty of a set of behavioural options to a clear and stable pattern of regular interaction. The results showed that the level of employees’ salaries is not crucial for overcoming shadow imports, but the level of integrity of customs officers is a more important indicator. The article shows that the mechanism of legalization of shadow operations (in particular, unorganized imports) should be based not only on economic but also on social parameters: the level of moral and professional principles of customs officers. The practical value of the research results is to improve the mechanisms of legalization of unorganized imports in Ukraine.

The Origins of Human Amenability to Propaganda

The author examines the main psychological characteristics of a person that have made him susceptible to the influence of other people, including propaganda. The subject of the study is these features of the human psyche. There are several main blocks of these psychological features: from imitation of parents and interaction in a team, where people are affected by mechanisms of deception and self-deception in order to convince others more effectively and rate themselves higher, to interaction within the social hierarchy, it is considered which strategies are more effective, and how this influences on the mechanisms of deception and self-deception. Using mathematical modeling methods, game theory and algorithms written in the python programming language, the author analyzes the most effective mechanisms of interaction among people in the social hierarchy, which contributed to the development of culture and deception, making a person more tricky. It is noted that the growth of what is commonly called "civility" is not so much a "herd" or "weakness", as it is sometimes estimated (the most famous example of such an assessment is Friedrich Nietzsche), as a trick, due to the fact that it is a more effective method of promotion in the social hierarchy and the struggle for power.

META-GAME THEORETIC ANALYSIS OF SOME STANDARD GAME THEORETIC PROBLEMS

Meta game theory is a non-quantitative reconstruction of mathematical game theory. This paper attempts to adapt meta-game theory for conflict analysis. A conflict is a situation where parties with opposing goals affect one another. A simple approach for performing meta-game analysis is adapted in this paper and illustrated on various games standard in game theory literature. The approach presented yields the desired results, although the computation required is much lesser than the standard Game theory analysis. Even a person without detailed knowledge about meta game analysis or game theory can implement this method.

Game-Theoretic Approach to Modeling Collective Labor Incentives for Regional Civil Servants in Russia

Currently, a number of external factors (in particular, sanctions pressure from the US and EU countries, the pandemic of a new coronavirus infection) have a strong negative impact on the socio-economic development of the constituent entities of the Russian Federation. Therefore, the head of almost any Russian region is forced to perform the functions of an anti-crisis manager. The modern system of stimulating the work of civil regional employees can help improve the efficiency of public administration, and as a result, ensure the socio-economic development of a constituent entity of the Russian Federation. The author's approach to this issue is based on the simultaneous application of a number of modern scientific methods, namely index, neural network technologies and mathematical game theory. The use of neural network technologies makes it possible to objectively assess the achieved level of socio-economic development of a constituent entity of the Russian Federation. Taking into account the positive foreign (Singapore and South Korean) experience in the field of civil service reform, it is proposed to make the amount of collective incentive payments (bonus fund) of regional civil servants directly dependent on the achieved level of socio-economic development of the subject of the Russian Federation. In turn, this implies the development of a hierarchical system of collective-individual stimulation of the work of regional civil servants. During the construction of the game-theoretic model, the correct establishment of the relationship between the level of collective incentive payments to regional civil servants and the socio-economic development of a constituent entity of the Russian Federation is ensured. After experimental refinement of the parameters of the game-theoretic model, there is a possibility of its practical application to stimulate the work of regional civil servants in Russia. The introduction of the author's approach into the practice of regional management, firstly, will allow coordinating the activities of ministries and departments, and secondly, will strengthen control over the targeted spending of budgetary funds on bonus payments to civil civil servants.

An Application of Game Theory to Beckett’s Waiting for Godot and Endgame

Abstract Waiting for Godot and Endgame are rich in terms of interaction between characters and their surrounding contexts. The present paper examines these interactions according to the mathematical theory of games proposed by Steven J. Brams in Divine Games: Game Theory and the Undecidability of a Superior Being. The framework of Search Decision is used to examine the differences between the two plays in terms of interaction between the “state of nature” and Person, which provides a clear understanding of the reasons behind strategies characters may take within uncertain environments.

Institutions: a promising topic insufficiently clarified

The basic question of sociology is what sets of rules and order are used in society and how they are maintained. One possible answer is based on the concept of institutions, which still provokes theoretical discussions due to, among other things, a certain ambiguity, since the term ‘institution’ is, figuratively speaking, shrouded in a kind of fog that prevents it from being captured in any direct, clear way. Today, ambitions of philosophy, political science, anthropology or mathematical game theory, which try to solve this problem outside the sociological framework, contribute to the deepening of the ambiguities surrounding the concept of institutions. Some approaches tend to define institutions as a cyber black box with inputs and outputs, whose working remains largely hidden (especially philosophical and mathematical approaches strive to find some common universal principle or even mathematical formula). From the perspective of general sociological theory, the article considers the topic of institutions. The author identifies this topic as a central issue that needs to be reconsidered in sociology. The starting point of the article is the analysis of concepts related to the topic, their definitions and paradigmatic integration. In the following part, the author considers the theoretical interpretations in the works of Peter Berger, Thomas Luckmann, John Searle, and the concepts inspired by game theories and rational behaviour theories. After that, ten basic issues of the current approaches are identified. The author pays particular attention to the fact that methodological individualism tends to dominate, which explains the ignorance of certain issues, especially of a holistic and macro-social nature, thus, leading to some problematic simplifications. The article shows what needs to be changed in the current social-scientific thinking on institutions in order to develop a more appropriate starting point for the further development of sociological theory.

Design of the Regional Healthcare Financing Mechanism

The significance of the influence of exogenous factors on the stability of the state of the socio-economic system (SES) necessitates the development of a methodological framework for regulating regional systems. One of the most important criteria for assessing the sustainability of the SES is the state of human capital, which assumes, first of all, the sufficiency of medical services in accordance with the necessary dynamics of the natural production of labor resources. The mathematical theory of games served as the basic theory of the formalization of the task of designing an economic mechanism. The model of the choice of the economic mechanism of the regional subsystem of healthcare is formulated in terms of the task of the design of the economy. The results of the research presented in the article summarize the author's ideas about the possibility of modeling the choice of an economic mechanism for financing a regional healthcare system that provides the required level of sustainability based on the sufficiency of financing for medical services. After evaluating the possibility of designing specific economic mechanisms, the presence of sustainable interaction between financing healthcare and the level of sustainable development of the region’s SES was substantiated.

Russia’s Arctic Strategy in the Greater Eurasian Partnership

This study focuses on the role of the Arctic Strategy of Russia in the Great Eurasian Partnership.Aim. The study aims to identify the features of the Arctic Strategy of Russia in the Great Eurasian Partnership.Tasks. The development of principles of geopolitical forecasting and work with big data, with the aim of synchronizing the integration processes contradictory in nature and interests of the actors in Greater Eurasia, identifying the features of the geopolitical regionalization of Eurasia, and analyzing the global security analytics of the Great Eurasian Partnership in the coming “digital era”.Methods. The transition from the “analog” to the “digital era” at the beginning of the 21st century meant an essentially revolution in the data itself, which was associated with the emergence of their new quality — predictive. The methodology for research and forecasting the prospects of Eurasian integration is modeling the multi-agent interaction of geopolitical factors of coalitions based on mathematical game theory. The strategy of transition to a polycentric world order implies the need to move from “geopolitical fiction” to geopolitics, based on mathematical modeling of global geopolitics processes using game theory methods.Results. The geopolitical regionalization of Eurasia is a challenge to time. On the expanses of the Eurasian continent, several multi-format long-term “Eurasian projects” are increasingly clearly emerging. This is, firstly, the Eurasian Economic Union, secondly, the Chinese One Belt-One Way and, thirdly, Indo-Pacifica. The Russian Arctic is a region of the Great Eurasian Partnership. The tasks of the modern Arctic policy of Russia are focused on ensuring the priority growth of raw materials exports and industrial development of the Arctic territories, rather than on solving the problems of improving the quality of life of the local population, although in the Russian Arctic strategy until 2035 these tasks are formulated quite correctly.Conclusion. The analytics of the Eurasian partnership and the wording of expert assessments should be formed on the basis not only of political discourse, but also of exact sciences. In modern conditions, the development of scenario projects for the construction of the Great Eurasian Partnership, which includes the Greater Arctic (which, in turn, require an independent theoretical and methodological study), involves the full use of the apparatus of mathematical geopolitics (game theory), scenario modeling and big data technologies.

An Anglian Alliance: Place-Name Tracing the Iclingas and Wicingas

Abstract This paper describes the close relationship between two obscure tribal groups, the Iclingas and the Wicingas. Starting on the Continent in Angeln and crossing over to East Anglia by different routes, they migrated across post-Roman Britain to the Western Midlands, where they provided mutual support in establishing the medieval kingdoms of Mercia and Hwiccia. Based upon the tracing of place-names and the mapping of settlements along historical migration routes, this research incorporates several disciplines, including medieval history, migration studies, and onomastics. The paper also makes use of innovative techniques, such as Micro-level Tracing and Contact Tracing, as well as modern tools, such as the Mathematical Theory of Games, and Google Maps, to describe the unexpected alliance between these two Anglian kinship groups, thereby adding significant information to the notoriously opaque history of Britain in the sixth century.

ОБ ОДНОЙ МОДИФИКАЦИИ РАВНОВЕСИЯ ПО НЭШУ

By the end of the last century there were four areas in the mathematical theory of positional differential games: non-coalitional positional differential games, cooperative, hierarchical and, finally, the least-understood coalitional positional differential games. In their turn, coalitional games are divided into games with transferable payoffs (games with side payments when players can split profits in the course of the game) and with non-transferable payoffs (games with side payments when there are no such distributions for this or that reason). The coalitional games with side payments are being extensively explored at the Faculties of Applied Mathematics and Management Processes of St. Petersburg University and the Institute of Mathematics and Information Technologies of Petrozavodsk State University (by Professors L.A. Petrosyan, V.V. Mozalov, E.M. Parilina, A.N. Rettieva and their numerous students). However, side payments are not always present even in economic cooperation; moreover, side payments can be legislated against. We believe that the research of the equilibrium of threats and counter-threats (sanctions and counter-sanctions) in non-coalitional differential games that we have carried out over the last years allows to also cover some aspects of non-transferable payoff coalitional games. The article considers the issues of namely the internal and external stability of coalitions in the class of positional differential games. The coefficient constraints were identified for the mathematical model of a linear-quadratic differential positional game with twin-coalitional structure for six persons where this coalitional structure is internally and externally stable.

On a new system of fractional delay differential equations coupled with fuzzy variational inequalities

Fuzzy variational inequalities (FVIs) are modeling tools used to characterize a variety of fuzzy decision making problems arising in mathematical optimization, control theory, operations research, and game theory. Fractional order delay differential equations are also finding applications in all disciplines including chemistry, physics, and finance. The aim of this paper is to introduce and study a new dynamical fuzzy system, named the fractional differential fuzzy variational inequality (FDFVI) with delay, which bridges these two areas of research and broadens the class of problems amenable to be studied under the fuzzy environments. By using the KKM theorem and monotonicity arguments, we show that the solution set of the FVI is nonempty, convex and compact. We also establish the upper semicontinuity of the solution mapping U of the FVI involved in the FDFVI with delay. Moreover, we obtain an existence of the mild solution for the FDFVI with delay by employing Bohnenblust-Karlin's fixed point theorem. In addition, we provide an approximating algorithm to find a solution of the FDFVI with delay. Finally, we give two numerical examples to illustrate our main results.

Application of cooperative game theory in a spatial context: An example of the application of the community-led local development instrument for the decision support system of biogas plants construction

The aim of the article is to develop a methodology for the creating decision support system by the integration of spatial, demographic and economic data and their processing with the use of game theory and spatial information modeling methods. The article proposes a novelty method for applying the mathematical theory of cooperative games to analyze the use of different types of public policy and shows which one is most profitable locally for a modern smart city and its three main stakeholders: Authorities, Business, and Citizens. The developed method supports effective cooperation in the “ABC triangle” – with EU funds reasonably. The research conducted on the illustrative construction of a local biogas plant in the commune of Żuromin showed the economic and social potential of the proposed model. Without loss of generality of the solution, the model may be used to support decision-making systems in the context of EU Policy Objective 5the thematically and spatially diverse CLLD instruments (Community-led Local Development, in regional development as well as the creation of smart cities and communities). According to our newest information within the commune of Żuromin, they are going to build two biogas plants. This situation is compliant with our findings.

At Lunch with Freeman Dyson

This is the story of a minor discovery in mathematical game theory. It concerns the prisoner’s dilemma game, which, played once, involves little strategy. But consider the iterated prisoner’s dilemma (IPD) game. In the IPD, there is information in the previous plays, which each player can use to devise a superior strategy that remains self-interested.

Strict Rules of Free Competition (about The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2020)

Studying the research results by Nobel prize-winning economists is a fundamentally important task for determining the most promising areas of development of Russian economic science. The author traces the connections between all these works and their predecessors’ work, many of whom were also awarded the Nobel prize in economics. Three lines of development of the predecessors’ achievements are identifid: information asymmetry, limited rationality, the design of market mechanism and new institutionalism. The article does not address the problems of auction theory related to its formal justifiation, which is part of mathematical economics and game theory. However, it is noted that this is an essential part of the laureates’ achievements. The article’s main conclusions are that the prize received for “improving the theory of auctions” fis into the broader economic research context. The winners solved the problems of maintaining free competition and reducing the market’s likelihood of monopolization. The author pays special attention to the results of the empirical analysis of actually implemented auctions. This analysis is divided into three parts, corresponding to the three stages of each auction: starting problems (distrust, the reputation of participants, etc.), the course of the auction (behaviour of participants and results, in particular, the “winner’s curse”.

Residential energy trading with blockchain technology

Blockchain technology is a peer-to-peer value transfer technology that guarantees the safety and correctness of transactions between parties who do not trust each other without a universally trusted entity. Because of this characteristic, we study possible integration of blockchain technology with a local neighborhood power grid, to design a truly decentralized energy trading market. The proposed design allows energy producers within the local power networks to safely transact with neighborhood households. In other words, the users who have a redundant amount of power can sell it to users who need power at a fairer price, than is offered by a utility company. We show that such local trades provide benefits to both electricity buyers and sellers. This paper does two things: (1) establishes a mathematical game theory model for the users’ decision to buy or sell power in the peer-to-peer energy market and (2) discuss blockchain software stack for deploying such a system. For the first part, we use a smart algorithm built upon KKT conditions to solve the multi-level game theory model. Secondly, we show how the electricity price offered by the central company is influenced by the introduction of the blockchain to the power transaction system. As supporting evidence we provide experimental data—the simulation of the market and its infrastructure using blockchain Hyperledger’s Fabric framework. Finally, we found that the electricity price can decrease dramatically by allowing peer-to-peer transactions among prosumers and consumers unless the amount of generating power from prosumers is much lower than their demand. We foresee a great future for the applications of blockchain technology in this area with the increasing mass adoption of solar and renewable generation at the consumer level. However, these processes will enact more discussions on power delivery grid ownership and its public access, usage, and management.