Operations Management - Game Theory, Goal Programming & Queuing Theory
Types of Games - Basic Concepts In Game Theory
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There are several classifications of a game. The classification may be based on various factors such as the number of participants, the gain or loss to each participant, the number of strategies available to each participant, etc.
Types of Games
There are several classifications of a game. The classification may be based on various factors such as the number of participants, the gain or loss to each participant, the number of strategies available to each participant, etc. Some of the important types of games are enumerated below.
In two person games, there are exactly two players and each competitor will have a finite number of strategies. If the number of players in a game exceeds two, then we refer to the game as n-person game.
If the sum of the payments to all the players in a game is zero for every possible outcome of the game, then we refer to the game as a zero sum game. If the sum of the payoffs from any play of the game is either positive or negative but not zero, then the game is called a non-zero sum game
A game of perfect information is the one in which each player can find out the strategy that would be followed by his opponent. On the other hand, a game of imperfect information is the one in which no player can know in advance what strategy would be adopted by the competitor and a player has to proceed in his game with his guess works only.
A game with a finite number of moves is the one in which the number of moves for each player is limited before the start of the play. On the other hand, if the game can be continued over an extended period of time and the number of moves for any player has no restriction, then we call it a game with unlimited number of moves.
If the sum of the game is not zero but the sum of the payoffs to both players in each case is constant, then we call it a constant sum game. It is possible to reduce such a game to a zero-sum game.
When the number of players in a game is two and each player has exactly two strategies, the game is referred to as 2x2 two person game.
A game in which the first player has precisely two strategies and the second player has three or more strategies is called an 2xn game.
A game in which the first player has three or more strategies and the second player has exactly two strategies is called an mx2 game.
When the number of players in a game is two and each player has exactly three strategies, we call it a 3x3 two person game.
Two-person zero sum games are said to be larger if each of the two players has 3 or more choices.
The examination of 3x3 and larger games is involves difficulties. For such games, the technique of linear programming can be used as a method of solution to identify the optimum strategies for the two players.
Consider a game with two players. If the sum of the payoffs to the two players is not constant in all the plays of the game, then we call it a non-constant game.
Such games are divided into negotiable or cooperative games and non-negotiable or non-cooperative games.
There are several classifications of a game. The classification may be based on various factors such as the number of participants, the gain or loss to each participant, the number of strategies available to each participant, etc. Some of the important types of games are enumerated below.
Two person games and n-person games
In two person games, there are exactly two players and each competitor will have a finite number of strategies. If the number of players in a game exceeds two, then we refer to the game as n-person game.
Zero sum game and non-zero sum game
If the sum of the payments to all the players in a game is zero for every possible outcome of the game, then we refer to the game as a zero sum game. If the sum of the payoffs from any play of the game is either positive or negative but not zero, then the game is called a non-zero sum game
Games of perfect information and games of imperfect information
A game of perfect information is the one in which each player can find out the strategy that would be followed by his opponent. On the other hand, a game of imperfect information is the one in which no player can know in advance what strategy would be adopted by the competitor and a player has to proceed in his game with his guess works only.
Games with finite number of moves / players and games with unlimited number of moves
A game with a finite number of moves is the one in which the number of moves for each player is limited before the start of the play. On the other hand, if the game can be continued over an extended period of time and the number of moves for any player has no restriction, then we call it a game with unlimited number of moves.
Constant-sum games
If the sum of the game is not zero but the sum of the payoffs to both players in each case is constant, then we call it a constant sum game. It is possible to reduce such a game to a zero-sum game.
2x2 two person game and 2xn and mx2 games
When the number of players in a game is two and each player has exactly two strategies, the game is referred to as 2x2 two person game.
A game in which the first player has precisely two strategies and the second player has three or more strategies is called an 2xn game.
A game in which the first player has three or more strategies and the second player has exactly two strategies is called an mx2 game.
3x3 and large games
When the number of players in a game is two and each player has exactly three strategies, we call it a 3x3 two person game.
The examination of 3x3 and larger games is involves difficulties. For such games, the technique of linear programming can be used as a method of solution to identify the optimum strategies for the two players.
Non-constant games
Consider a game with two players. If the sum of the payoffs to the two players is not constant in all the plays of the game, then we call it a non-constant game.
Such games are divided into negotiable or cooperative games and non-negotiable or non-cooperative games.
Tags : Operations Management - Game Theory, Goal Programming & Queuing Theory
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