Several of the key concepts used in the theory of games are described below:
Key concepts in the Theory
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.
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
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.
The tabular display of the
payoffs to players under various alternatives is called the payoff matrix of
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
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
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
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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