Wyniki wyszukiwania - BazTech

1

Equilibrium stacks for a non-cooperative game defined on a product of staircase-function continuous and finite strategy spaces

Romanuke Vadim

Journal of Mathematics and Applications

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2023

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Vol. 46

79--114

EN

A method of solving a non-cooperative game defined on a product of staircase-function strategy spaces is presented. The spaces can be finite and continuous as well. The method is based on stacking equilibria of “short” non-cooperative games, each defined on an interval where the pure strategy value is constant. In the case of finite non-cooperative games, which factually are multidimensional-matrix games, the equilibria are considered in general terms, so they can be in mixed strategies as well. The stack is any combination (succession) of the respective equilibria of the “short” multidimensional-matrix games. Apart from the stack, there are no other equilibria in this “long” (staircase-function) multidimensional-matrix game. An example of staircase-function quadmatrix game is presented to show how the stacking is fulfilled for a case of when every “short” quadmatrix game has a single pure-strategy equilibrium. The presented method, further “breaking” the initial staircase-function game into a succession of “short” games, is far more tractable than a straightforward approach to solving directly the “long” non-cooperative game would be.

2

Proposition of multi-agent conflict situation simulation and reinforcement learning toolset with demonstration of early stage implementation

Jarosz Robert

Computer Science and Mathematical Modelling

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2023

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No. 17

13--22

EN

This paper introduces conceptual approach to modelling conflicts. A flexible framework compatible in development phase is presented. Model scalability, possibility of parallelization and computational distribution over network is discussed. As example of application there are presented two variants of classic game theory problems. At the end of the paper current problems are briefly stated and future work direction is presented.

PL

W artykule opisano koncepcję biblioteki do symulacji interakcji między graczami rozpatrującymi sytuacje konfliktowe. Opisano w nim założenia, w tym wymagania funkcjonalne dla oprogramowania. Przedstawiono proponowane rozwiązanie i wstępną wersję implementacji wraz z przykładami zastosowania koncepcji w klasycznych problemach teorii gier.

3

Kiedy można wygrać i jak wtedy grać, żeby wygrać?

Słanina Piotr

MINUT Matematyka i Informatyka na Uczelniach Technicznych

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2022

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Nr 4

1-15

PL

ednym z głównych problemów w grze kombinatorycznej jest wskazanie gracza, który jest w stanie zapewnić sobie zwycięstwo (tak zwane rozwiązanie gry). Jeżeli już to się uda, to czasami nadal nie będziemy w stanie wskazać temu graczowi, jak ma grać, aby wygrać. W tym artykule czytelnik zapozna się z najpopularniejszymi matematycznymi narzędziami, stosowanymi przy poszukiwaniu najlepszych strategii w grach kombinatorycznych. Ich opisy będą uzupełnione o przykłady gier. Będą się one pojawiały według stopnia trudności ich rozwiązania od najłatwiejszych do nierozwązanych po dzień dzisiejszy.

4

Time-unit shifting in 2-person games played in finite and uncountably infinite staircase-function spaces

Romanuke Vadim

Journal of Mathematics and Applications

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2022

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Vol. 45

133--179

EN

A computationally efficient and tractable method is presented to find the best equilibrium in a finite 2-person game played with staircase-function strategies. The method is based on stacking equilibria of smaller-sized bimatrix games, each defined on a time unit where the pure strategy value is constant. Every pure strategy is a staircase function defined on a time interval consisting of an integer number of time units (subintervals). If a time-unit shifting happens, where the initial time interval is narrowed by an integer number of time units, the respective equilibrium solution of any “narrower” subgame can be taken from the “wider” game equilibrium. If the game is uncountably infinite, i. e. a set of pure strategy possible values is uncountably infinite, and all time-unit equilibria exist, stacking equilibria of smaller-sized 2-person games defined on a rectangle works as well.

5

Multi-criteria multi-stage game optimization

Lisowski Józef

Journal of Automation, Electronics and Electrical Engineering

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2022

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Vol. 4, No. 1

37--42

EN

The article presents a mathematical model of a multi-stage game of the process of safe control of a transport object in possible collision situations with other encountered objects, containing a description of state variables, state and control constraints, and sets of permissible object strategies. Multi-criteria optimization tasks were formulated in the form of positional and matrix games under the conditions of playing non-cooperative and cooperative control as well as non-game optimal control. The multi-criteria control algorithms corresponding to these tasks were computer simulated in Matlab / Simulink on the example of a real situation.

PL

W artykule przedstawiono model matematyczny wieloetapowej gry procesu bezpiecznego sterowania obiektem transportowym w możliwych sytuacjach kolizyjnych z innymi spotkanymi obiektami, zawierający opis zmiennych stanu, ograniczeń stanu i sterowania oraz zbiory dopuszczalnych strategii obiektów. Sformułowano wielokryterialne zadania optymalizacyjne w postaci gry pozycyjnej i macierzowej, w warunkach rozgrywającego sterowania niekooperacyjnego i kooperacyjnego oraz nierozgrywającego sterowania optymalnego. Algorytmy sterowania wielokryterialnego odpowiadające tym zadaniom poddano symulacji komputerowej w programie Matlab/Simulink na przykładzie rzeczywistej sytuacji.

6

Solving Infinite Games in the Baire Space

Brütsch Benedikt, Thomas Wolfgang

Fundamenta Informaticae

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2022

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Vol. 186, nr 1-4

63--88

EN

Infinite games (in the form of Gale-Stewart games) are studied where a play is a se- quence of natural numbers chosen by two players in alternation, the winning condition being a subset of the Baire space ωω . We consider such games defined by a natural kind of parity au- tomata over the alphabet N, called N-MSO-automata, where transitions are specified by monadic second-order formulas over the successor structure of the natural numbers. We show that the classical Büchi-Landweber Theorem (for finite-state games in the Cantor space 2ω) holds again for the present games: A game defined by a deterministic parity N-MSO-automaton is deter- mined, the winner can be computed, and an N-MSO-transducer realizing a winning strategy for the winner can be constructed.

7

Optimizing the interaction between two closed-loop supply chains based on inverse logistics using the game theory method

Trung Nguyen Dinh, Huy Dinh Tran Ngoc, Chetthamrongchai Paitoon, Mohsen Karrar Shareef, Iskandar Ahmad Syarief, Nurjaya A., Sunarsi Denok, Singh Krishanveer, Chupradit Supat

Foundations of Computing and Decision Sciences

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2022

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Vol. 47, No. 4

455--467

EN

Over the past few years, attention to environmental problems, legal necessities, and economic advantages emerging from reproduction activities has attracted attention to reverse logistics activities in the form of a closed-loop supply chain, whether in industry or scientific research. The current study aims to model competitiveness and comparison between two closed-loop three-level supply chains, each of which includes a manufacturer, a retailer, and a third party to collect the products used by the customer, taking into account the concepts of game theory and the existence of aggregates. Moreover, a separate supplier for each chain is considered. In the forward supply chain, the manufacturer produces new products using new components or re-used products that have been collected from the consumer, then sells these products mainly to the retailer, and the retailer sells them. In the reverse chain, the collector provides the used products to the manufacturer after collection. The study utilized the definitions and concepts of game theory to model this closed loop chain as a Stackelberg game to obtain the optimal value of wholesale and retail price and the optimal value of the product return coefficient for the collector. Finally, the models based on some numerical examples are solved. Given the results, the remanufacturing costs have a significant role in making more profits for all members in such chains, and competitive chains should attempt to remanufacture the products at lower costs.

8

Equilibrium stacks for a three-person game on a product of staircase-function continuous and finite strategy spaces

Romanuke Vadim

Foundations of Computing and Decision Sciences

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2022

|

Vol. 47, No. 1

27--64

EN

A method of solving a three-person game defined on a product of staircase-function strategy spaces is presented. The spaces can be finite and continuous. The method is based on stacking equilibria of “short” three-person games, each defined on an interval where the pure strategy value is constant. In the case of finite three-person games, which factually are trimatrix games, the equilibria are considered in general terms, so they can be in mixed strategies as well. The stack is any interval-wise combination (succession) of the respective equilibria of the “short” trimatrix games. Apart from the stack, there are no other equilibria in this “long” trimatrix game. An example is presented to show how the stacking is fulfilled for a case of when every “short” trimatrix game has a pure-strategy equilibrium. The presented method, further “breaking” the initial “long” game defined on a product of staircase-function finite spaces, is far more tractable than a straightforward approach to solving directly the “long” trimatrix game would be.

9

Throwback

Gambarelli Gianfranco

Control and Cybernetics

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2022

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Vol. 51, No. 2

125--130

EN

With this short composition, I’d like to share with you a few events of my scientific life.

10

Overview of selected reinforcement learning solutions to several game theory problems

Jarosz Robert

Computer Science and Mathematical Modelling

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2022

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No. 15-16

13--22

EN

This paper collects several applications of reinforcement learning in solving some problems related to game theory. The methods were selected to possibly show variety of problems and approaches. Selections includes Thompson Sampling, Q-learning, DQN and AlphaGo Zero using Monte Carlo Tree Search algorithm. Paper attempts to show intuition behind proposed algorithms with shallow explaining of technical details. This approach aims at presenting overview of the topic without assuming deep knowledge about statistics and artificial intelligence.

PL

Artykuł gromadzi wybrane podejścia do rozwiązania problemów z teorii gier wykorzystując uczenie ze wzmocnieniem. Zastosowania zostały dobrane tak, aby przedstawić możliwie przekrojowo klasy problemów i podejścia do ich rozwiązania. W zbiorze wybranych algorytmów znalazły się: próbkowanie Thompsona, Q-learning (Q-uczenie), DQN, AlphaGo Zero. W artykule nacisk położono na przedstawienie intuicji sposobu działania algorytmów, koncentrując się na przeglądzie technologii zamiast na technicznych szczegółach.

11

Analysis of selected reinforcement learning applications in contract bridge

Jarosz Robert

Computer Science and Mathematical Modelling

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2022

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No. 15-16

23--31

EN

This paper presents an overview of four selected solutions addressing problem of bidding in card game of contract bridge. In the beginning the basic rules are presented along with basic problem size estimation. Brief description of collected work is presented in chronological order, tracking evolution of approaches to the problem. While presenting solution a short description of mathematical base is attached. In the end a comparison of solution is made, followed by an attempt to estimate future development of techniques.

PL

Artykuł przedstawia cztery wybrane podejścia do rozgrywania licytacji w brydżu. W części pierwszej przybliżane są zasady brydża, stanu wiedzy na jego temat oraz krótkie oszacowanie poziomu komplikacji problemu. W części zasadniczej przedstawiono krótkie opisy podejść badaczy do problemu licytacji, badania przedstawione są w kolejności chronologicznej, ukazując ewolucję podejść do problemu. W trakcie opisywania rozwiązań, przybliżane są po krótce matematyczne zasady działania wykorzystanych mechanizmów uczenia maszynowego. Część końcowa podsumowuje przedstawione porównanie rozwiązań i oszacowanie kierunku przyszłego rozwoju.

12

Multiobjective optimiaztion of microstructure parameters in a thermoelastic porous material by means of differential evolution and elements of game theory

Długosz Adam, Schlieter Tomasz

Computer Methods in Materials Science

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2022

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Vol. 22, No. 3

117--124

EN

The paper is devoted to the optimization of the microstructure parameters of a porous medium under thermo-mechanical loading. Four different criteria related to the properties of the porous material have been proposed and numerically implemented. To solve a multiobjective problem, a novel method based on the coupling of differential evolution and elements of game theory is used. The proposed algorithm features an appropriate balance between exploration and exploitation of objective space, which is necessary for the successful optimization of these types of tasks with the use of numerical simulations. The model of the thermo-elastic porous material is composed of two-scale direct analysis based on a numerical homogenization. Direct thermoelastic analysis with representative volume element (RVE) and finite element method (FEM) is performed. Numerical example of the optimization illustrating the usefulness of the proposed method is included.

13

Computational intelligence in marine control engineering education

Lisowski Józef

Polish Maritime Research

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2021

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nr 1

163--172

EN

This paper presents a new approach to the existing training of marine control engineering professionals using artificial intelligence. We use optimisation strategies, neural networks and game theory to support optimal, safe ship control by applying the latest scientific achievements to the current process of educating students as future marine officers. Recent advancements in shipbuilding, equipment for robotised ships, the high quality of shipboard game plans, the cost of overhauling, dependability, the fixing of the shipboard equipment and the requesting of the safe shipping and environmental protection, requires constant information on recent equipment and programming for computational intelligence by marine officers. We carry out an analysis to determine which methods of artificial intelligence can allow us to eliminate human subjectivity and uncertainty from real navigational situations involving manoeuvring decisions made by marine officers. Trainees learn by using computer simulation methods to calculate the optimal safe traverse of the ship in the event of a possible collision with other ships, which are mapped using neural networks that take into consideration the subjectivity of the navigator. The game-optimal safe trajectory for the ship also considers the uncertainty in the navigational situation, which is measured in terms of the risk of collision. The use of artificial intelligence methods in the final stage of training on ship automation can improve the practical education of marine officers and allow for safer and more effective ship operation.

14

Zero-sum games on a product of staircase-function finite spaces

Romanuke Vadim

Journal of Mathematics and Applications

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2021

|

Vol. 44

75--91

EN

A tractable method of solving zero-sum games defined on a product of staircase-function finite spaces is presented. The method is based on stacking solutions of “smaller” matrix games, each defined on an interval where the pure strategy value is constant. The stack is always possible, even when only time is discrete, so the set of pure strategy possible values can be continuous. Any combination of the solutions of the “smaller” matrix games is a solution of the initial zero-sum game.

15

A communication network routing problem: Modeling and optimization using non-cooperative game theory

Dubey Sapana P., Kedar Ganesh D., Ghate Suresh H.

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 1

155--164

EN

We consider a communication network routing problem wherein a number of users need to efficiently transmit their throughput demand in the form of data packets (incurring less cost and less delay) through one or more links. Using the game theoretic perspective, we propose a dynamic model which ensures unhindered transmission of data even in the case where the capacity of the link is exceeded. The model incorporates a mechanism in which users are appropriately punished (with additional cost) when the total data to be transmitted exceeds the capacity of the link. The model has multiple Nash equilibrium points. To arrive at rational strategies, we introduce the concept of focal points and get what is termed focal Nash equilibrium (FNE) points for the model. We further introduce the concept of preferred focal Nash equilibrium (PFNE) points and find their relation with the Pareto optimal solution for the model.

16

Acceptable-and-attractive Approximate Solution of a Continuous Non-Cooperative Game on a Product of Sinusoidal Strategy Functional Spaces

Romanuke Vadim

Foundations of Computing and Decision Sciences

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2021

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Vol. 46, No. 2

173--197

EN

A problem of solving a continuous noncooperative game is considered, where the player’s pure strategies are sinusoidal functions of time. In order to reduce issues of practical computability, certainty, and realizability, a method of solving the game approximately is presented. The method is based on mapping the product of the functional spaces into a hyperparallelepiped of the players’ phase lags. The hyperparallelepiped is then substituted with a hypercubic grid due to a uniform sampling. Thus, the initial game is mapped into a finite one, in which the players’ payoff matrices are hypercubic. The approximation is an iterative procedure. The number of intervals along the player’s phase lag is gradually increased, and the respective finite games are solved until an acceptable solution of the finite game becomes sufficiently close to the same-type solutions at the preceding iterations. The sufficient closeness implies that the player’s strategies at the succeeding iterations should be not farther from each other than at the preceding iterations. In a more feasible form, it implies that the respective distance polylines are required to be decreasing on average once they are smoothed with respective polynomials of degree 2, where the parabolas must be having positive coefficients at the squared variable.

17

Analysis of the main body behaviour of non-point source pollution control based on multimodal game model

Li Xin, Shang Jie

Ecological Chemistry and Engineering. S

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2021

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Vol. 28, nr 4

563--579

EN

The issue of agricultural non-point source pollution has attracted the attention of the state and the masse. In the non-point source pollution control organizations which composed of the governments, farmers and fertiliser sellers, due to the characteristics of rational economic body, the phenomenon of ”market failure” and ”government failure” may occur in the process of non-point source pollution control. In this paper, the author applies game theory to analyse the main behaviour characteristics of the three main bodies, and constructs the incomplete information dynamic game model that the government, farmers and fertiliser sellers participate in. According to the results of the equilibrium solution of the Haysani Axiom model, it is found that the decisions made by the three bodies of the government, the fertiliser seller and the farmer in the behaviour choice stage have a great influence on the behaviour choice of the other two bodies, and the process of each strategy choice by the three bodies is a dynamic game process of the three bodies. Finally, according to the main influencing factors reflected in the equilibrium solution, proposed the related non-point source pollution control countermeasure suggestion to the government main body.

18

Applying chaos theory to risk management in a game of chance

Jóźwiak Ireneusz J., Mariański Aleksander, Switana Jan, Szczepanik Michał

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2020

|

z. 144

195--211

EN

Purpose: The purpose of the paper is to illustrate the usage of techniques known from chaos theory to analyze the risk Design/methodology/approach: In this case the objects of application are winnings graphs of different poker players. Two types of players are presented; winning players (those with positive expected value) and breaking even players (expected value close to zero). Findings: Charts were analyzed with a fractal dimension calculated with the box method. Originality/value: Relation between fractal dimension and Hurst exponent is shown. Relation between risk in sense of chaos theory and players’ long-term winning is also described. Further applications of chaos theory to analyze the risk in games of chance are also proposed.

19

Game theory analysis in Indonesia’s shipping industry: Case study agreement between PT. X and PT. Y

Susanto Heru

Scientific Journal of Gdynia Maritime University

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2020

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nr 113

7--16

EN

Nowadays, the container shipping industry in Indonesia has a tendency to oligopoly, even in one shipping route. Two big shipping liners in Indonesia, PT. X and PT. Y, have been dominating sales on the Surabaya-Banjarmasin route. The aim of this study is to know how the liners behave in an oligopoly, making decisions that are profitable for both parties. The agreement on challenge, competition, and cooperation between PT. X and PT. Y in serving shipping services is the main focus in this study. The methodology used is a game theory approach to show the possible strategies in rates and supply competition. The result shows that the agreement between PT. X and PT. Y consisted of price decision and supply quantity. The price decision is rated at a lower price of USD 300/TEU where P = MC which has no incentive. While the agreement on supply quantity is 26.000 TEUs in total. Moreover, the cooperative agreement between the shipping liners is a joint allience which not depend on each capacity ratio.

20

Multi-criteria optimisation of multi-stage positional game of vessels

Lisowski Józef

Polish Maritime Research

|

2020

|

nr 1

46--52

EN

The paper presents a mathematical model of a positional game of the safe control of a vessel in collision situations at sea, containing a description of control, state variables and state constraints as well as sets of acceptable ship strategies, as a multi-criteria optimisation task. The three possible tasks of multi-criteria optimisation were formulated in the form of non-cooperative and cooperative multi-stage positional games as well as optimal non-game controls. The multicriteria control algorithms corresponding to these tasks were subjected to computer simulation in Matlab/Simulink software based on the example of the real navigational situation of the passing of one’s own vessel with eighteen objects encountered in the North Sea.