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

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

Romanuke Vadim

Journal of Mathematics and Applications

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2021

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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.

3

Sensitivity of computer support game algorithms of safe ship control

Lisowski J.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 2

439--446

EN

The paper investigates the sensitivity of safe ship control to inaccurate data from the ARPA anti-collision radar system and to changes in the process control parameters. The system structure of safe ship control in collision situations and computer support programmes exploring information from the ARPA anti-collision radar are presented. Sensitivity characteristics of the multistage positional non-cooperative and cooperative game and kinematics optimization control algorithms are determined through examples of navigational situations with restricted visibility at sea.

4

Problem śledzenia ruchomego celu przez grupę robotów - wykorzystanie

Skrzypczyk K.

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2006

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z. 38

191-208

PL

W pracy przedstawiono problem śledzenia ruchomego celu przez grapę robotów mobilnych. Zaprezentowano metodę sterowania ruchem poszczególnych robotów, wykorzystującą gry macierzowe o sumie niezerowej. Zaprezentowano również strukturę scentralizowanego systemu sterowania w ramach, którego rozważany jest omawiany problem. W pracy przedyskutowano użycie koncepcji równowagi Nasha do rozwiązania modelowanego problemu oraz przedstawiono metodę arbitrażu pozwalającą na wybór pojedynczego rozwiązania, w przypadku gdy istnieją rozwiązania wielokrotne. Przedstawiono również wyniki przeprowadzonych symulacji.

EN

In this paper a problem of tracking a moving target by a team of mobile robots is presented. A method of control of individual team-mates based on non-zero sum, one-stage game in a normal form is proposed. The architecture of the control system, with a real-time planner based on centralized sensory system is presented in the paper. The use of non-cooperative solution concepts like the Nash equilibrium and min-max safety strategy is discussed. An arbiter module is used to provide unique control for individual team-mates, and to ensure "fair" distribution of costs among roots. A results of simulation that was carried out is also presented to show an effectiveness of proposed approach.