The Two-person, Zero-sum Game

Introduction: In game theory we have some strategy in the game rules which is depending upon the adoption of the players. Theory of games or decision theory is also the part of operation management in which two or more than two industrial units are involved under conflict condition.

 The two person, zero-sum game: (Pure Strategy and Mixed Strategy games):

•         In one of the most preferred position for each player is achieved by adopting a single strategy. Hence this game is known as pure strategy game.
•         The second type requires the adoption by both players of a mixture or a combination of different strategies as opposed to a single strategy. Therefore this is termed as mixed strategy game.
•        In pure strategy game is a decision rule always to select the same course of action.
•        Every course of action is pure strategy.
•         A mixed strategy is that in which a player decides, in advance to choose one of his course of action in accordance with some fixed probability distribution.
• In case of mixed strategy we associate probability to each course of action (each pure strategy).
•        The pure strategies, which are used in mixed strategy game with non-zero probabilities, are termed as supporting strategies. Mathematically, a mixed strategy to any player is an ordered set of ‘m’ non-negative real numbers, which add to a sum unity (m is the number of pure strategies available to a player).

Characteristics of the game:

Type of course of action or strategy:

•         The purpose of the game theory is to determine the best strategies for each player on the basis of maximin and minimax criterion of optimality.
•          In this criterion a player lists his worst possibleoutcomes and then he chooses that strategy which corresponds to the best of those worst outcomes.
•          The value of the game is the maxim guaranteed gain to player. The value is denoted by ‘v’. The game whose value v = 0 is known as zero sum game or fair game.
•          Solving the game mean to find the best strategies for both the players and find the value of the game.
• The game theory does not insist on how a game should he played, but only tells the procedure and principles by which the action should be selected. Hence, the game theory is a decision theory useful in competitive situations.
•        The fundamental theorem assures that there exists a solution andthe value of a rectangular game in terms of mixed strategies.
•          To classify the games, they are: Number of persons or groups who are involved in playing the game Number of strategies or courses of action each player or group has (they may be finite or infinite).