Operations Management - Game Theory, Goal Programming & Queuing Theory
Key concepts in the Theory of Games
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Several of the key concepts used in the theory of games are described below:
Key concepts in the Theory
of Games
Several of the key concepts used in the theory of games are described below:
The competitors or decision makers in a game are called the players of the game.
The alternative courses of action available to a player are referred to as his strategies.
The outcome of playing a game is called the pay off to the concerned player.
A strategy by which a player can achieve the best pay off is called the optimal strategy for him.
A game in which the total payoffs to all the players at the end of the game is zero is referred to as a zero-sum game.
Games with “less than complete conflict of interest” are called non-zero sum games. The problems faced by a large number of business organizations come under this category. In such games, the gain of one player in terms of his success need not be completely at the expense of the other player.
The tabular display of the payoffs to players under various alternatives is called the payoff matrix of the game.
If the game is such that each player can identify one and only one strategy as the optimal strategy in each play of the game, then that strategy is referred to as the best strategy for that player and the game is referred to as a game of pure strategy or a pure game.
If there is no one specific strategy as the ‘best strategy’ for any player in a game, then the game is referred to as a game of mixed strategy or a mixed game. In such a game, each player has to choose different alternative courses of action from time to time.
A game in which N-players take part is called an N-person game.
The maximum of the minimum gains is called the maximin value of the game and the corresponding strategy is called the maximin strategy. Similarly the minimum of the maximum losses is called the minimax value of the game and the corresponding strategy is called the minimax strategy. If both the values are equal, then that would guarantee the best of the worst results.
If the game is such that the players are taken to cooperate on any or every action which may increase the payoff of either player, then we call it a negotiable or cooperative game.
If the players are not permitted for coalition then we refer to the game as a non-negotiable or non-cooperative game.
A saddle point of a game is that place in the payoff matrix where the maximum of the row minima is equal to the minimum of the column maxima. The payoff at the saddle point is called the value of the game and the corresponding strategies are called the pure strategies.
One of the strategies of either player may be inferior to at least one of the remaining ones. The superior strategies are said to dominate the inferior ones.
Several of the key concepts used in the theory of games are described below:
Players
The competitors or decision makers in a game are called the players of the game.
Strategies
The alternative courses of action available to a player are referred to as his strategies.
Pay off
The outcome of playing a game is called the pay off to the concerned player.
Optimal Strategy
A strategy by which a player can achieve the best pay off is called the optimal strategy for him.
Zero-sum game
A game in which the total payoffs to all the players at the end of the game is zero is referred to as a zero-sum game.
Non-zero sum game
Games with “less than complete conflict of interest” are called non-zero sum games. The problems faced by a large number of business organizations come under this category. In such games, the gain of one player in terms of his success need not be completely at the expense of the other player.
Payoff matrix
The tabular display of the payoffs to players under various alternatives is called the payoff matrix of the game.
Pure strategy
If the game is such that each player can identify one and only one strategy as the optimal strategy in each play of the game, then that strategy is referred to as the best strategy for that player and the game is referred to as a game of pure strategy or a pure game.
Mixed strategy
If there is no one specific strategy as the ‘best strategy’ for any player in a game, then the game is referred to as a game of mixed strategy or a mixed game. In such a game, each player has to choose different alternative courses of action from time to time.
N-person game
A game in which N-players take part is called an N-person game.
Maximin-Minimax Principle
The maximum of the minimum gains is called the maximin value of the game and the corresponding strategy is called the maximin strategy. Similarly the minimum of the maximum losses is called the minimax value of the game and the corresponding strategy is called the minimax strategy. If both the values are equal, then that would guarantee the best of the worst results.
Negotiable or cooperative game
If the game is such that the players are taken to cooperate on any or every action which may increase the payoff of either player, then we call it a negotiable or cooperative game.
Non-negotiable or non-cooperative game
If the players are not permitted for coalition then we refer to the game as a non-negotiable or non-cooperative game.
Saddle point
A saddle point of a game is that place in the payoff matrix where the maximum of the row minima is equal to the minimum of the column maxima. The payoff at the saddle point is called the value of the game and the corresponding strategies are called the pure strategies.
Dominance
One of the strategies of either player may be inferior to at least one of the remaining ones. The superior strategies are said to dominate the inferior ones.
Tags : Operations Management - Game Theory, Goal Programming & Queuing Theory
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