The game theory was firstly used for description of economic phenomena and social interaction. But there are certain type of perfect information games （PI-games）, the so-called positional game or Banach-Mazur games,...The game theory was firstly used for description of economic phenomena and social interaction. But there are certain type of perfect information games （PI-games）, the so-called positional game or Banach-Mazur games, which so far have not been applied in economy. The perfect information positional game is defined as the game during which at any time the choice is made by one of the players who is acquainted with the previous decision of his opponent. The game is run on a sequential basis. The aim of this paper is to discuss selected Banach-Mazur games and to present some applications of positional game. This paper also shows new theoretical example of a determined PI-game, based by theoretical overview. All considerations are pure theoretical and based by logical deduction.展开更多
Infinite game is a power tool in studying various objects and finding descriptions of some properties of filters in mathematics.Game-theoretic characterizations for meager filters,Q-filters and Ramsey filters were obt...Infinite game is a power tool in studying various objects and finding descriptions of some properties of filters in mathematics.Game-theoretic characterizations for meager filters,Q-filters and Ramsey filters were obtained by Tomek Bartoszynski,Claude Laflamme and Marion Scheepers.In this paper,the authors obtain two game-theoretic characterizations for rapid filters onω.展开更多
文摘The game theory was firstly used for description of economic phenomena and social interaction. But there are certain type of perfect information games （PI-games）, the so-called positional game or Banach-Mazur games, which so far have not been applied in economy. The perfect information positional game is defined as the game during which at any time the choice is made by one of the players who is acquainted with the previous decision of his opponent. The game is run on a sequential basis. The aim of this paper is to discuss selected Banach-Mazur games and to present some applications of positional game. This paper also shows new theoretical example of a determined PI-game, based by theoretical overview. All considerations are pure theoretical and based by logical deduction.
基金supported by the National Natural Science Foundation of China(No.11771311)。
文摘Infinite game is a power tool in studying various objects and finding descriptions of some properties of filters in mathematics.Game-theoretic characterizations for meager filters,Q-filters and Ramsey filters were obtained by Tomek Bartoszynski,Claude Laflamme and Marion Scheepers.In this paper,the authors obtain two game-theoretic characterizations for rapid filters onω.
