Game theory
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'''Game Theory''' is the study of situations where multiple decision-makers influence one another. Game theory is comprised of two main branches, [[cooperative game theory]] and [[non-cooperative game theory]]. A [[cooperative game]] is a game where the players form alliances with each other making agreements among each other. Cooperative games could be used to model interactions among designers working together on a common systems integration project. In contrast, [[non-cooperative games]] involve self-interested players. Non-cooperative games could be used to model market competition among profit-seeking firms. | '''Game Theory''' is the study of situations where multiple decision-makers influence one another. Game theory is comprised of two main branches, [[cooperative game theory]] and [[non-cooperative game theory]]. A [[cooperative game]] is a game where the players form alliances with each other making agreements among each other. Cooperative games could be used to model interactions among designers working together on a common systems integration project. In contrast, [[non-cooperative games]] involve self-interested players. Non-cooperative games could be used to model market competition among profit-seeking firms. | ||
| - | + | =Assumptions= | |
#Each player has at least two choices | #Each player has at least two choices | ||
#Each combination of choices leads to either a win, loss, or draw each with an assigned payoff | #Each combination of choices leads to either a win, loss, or draw each with an assigned payoff | ||
| Line 7: | Line 7: | ||
#Each player will select the choice that will give the higher payoff | #Each player will select the choice that will give the higher payoff | ||
| - | + | =Terminology= | |
| + | |||
==Payoff== | ==Payoff== | ||
Payoff is a number that represents gains or losses of players. | Payoff is a number that represents gains or losses of players. | ||
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*a positive nummber represents gain | *a positive nummber represents gain | ||
| - | + | ==Symmetric Game== | |
Symmetric game is a game where the identity of the player does not change the results of the game. An example of a symmetric game would be a game of chicken. | Symmetric game is a game where the identity of the player does not change the results of the game. An example of a symmetric game would be a game of chicken. | ||
| - | *A game of chicken involves two fools driving towards each other on a road. The first one to swerve is the loser and if neither swerve, they die. | + | *A game of chicken involves two fools driving towards each other on a road. The first one to swerve is the loser and if neither swerve, they die. The following table shows a payoff matrix of a Game of Chicken. |
| - | [[ | + | [[Image:chicken_game.gif]] |
| - | |||
| - | + | ==Zero Sum Game== | |
Zero sum game is a game in which for one player to benefit, another has to lose. The sum of the player's payoff is zero. An example of a zero sum game is a game of rock paper scissors. | Zero sum game is a game in which for one player to benefit, another has to lose. The sum of the player's payoff is zero. An example of a zero sum game is a game of rock paper scissors. | ||
| - | *A game of rock paper scissors involves the players to make three hand gestures: a rock, paper and scissors. Rock beats scissors, scissors beat paper, and paper beats rock. If the gestures are the same, the game is tied. | + | *A game of rock paper scissors involves the players to make three hand gestures: a rock, paper and scissors. Rock beats scissors, scissors beat paper, and paper beats rock. If the gestures are the same, the game is tied. The following table shows the payoff matrix of a game of Rock Paper Scissors. |
| - | [[ | + | [[Image:rock_paper_scissor.gif]] |
| - | |||
| - | + | ==Complete Information== | |
The concept of complete information is that each of the players know all the optimal strategies and payoffs of the other player. | The concept of complete information is that each of the players know all the optimal strategies and payoffs of the other player. | ||
| - | + | ==Equilibrium Point== | |
| - | Equilibrium point, | + | Equilibrium point, or called [[Nash equilibrium]] point, is a point such that each player has chosen the optimal selection given the decision of the other players. |
| - | + | =See Also= | |
| - | *[[Cooperative | + | *[[Cooperative game]] |
| - | *[[Nash | + | *[[Nash equilibrum]] |
| - | *[[Non-cooperative | + | *[[Non-cooperative game]] |
| - | == | + | =External Links= |
| + | *Paul Walker, [http://www.econ.canterbury.ac.nz/personal_pages/paul_walker/gt/hist.htm A Chronology of Game Theory]. | ||
*http://www.gametheory.net/dictionary/Games/SymmetricGame.html | *http://www.gametheory.net/dictionary/Games/SymmetricGame.html | ||
*http://en.wikipedia.org/wiki/Game_theory | *http://en.wikipedia.org/wiki/Game_theory | ||
Current revision
Game Theory is the study of situations where multiple decision-makers influence one another. Game theory is comprised of two main branches, cooperative game theory and non-cooperative game theory. A cooperative game is a game where the players form alliances with each other making agreements among each other. Cooperative games could be used to model interactions among designers working together on a common systems integration project. In contrast, non-cooperative games involve self-interested players. Non-cooperative games could be used to model market competition among profit-seeking firms.
Contents |
Assumptions
- Each player has at least two choices
- Each combination of choices leads to either a win, loss, or draw each with an assigned payoff
- Each player knows the rules of the game
- Each player will select the choice that will give the higher payoff
Terminology
Payoff
Payoff is a number that represents gains or losses of players.
- a negative number represents loss
- 0 represents neither gain nor loss
- a positive nummber represents gain
Symmetric Game
Symmetric game is a game where the identity of the player does not change the results of the game. An example of a symmetric game would be a game of chicken.
- A game of chicken involves two fools driving towards each other on a road. The first one to swerve is the loser and if neither swerve, they die. The following table shows a payoff matrix of a Game of Chicken.
Zero Sum Game
Zero sum game is a game in which for one player to benefit, another has to lose. The sum of the player's payoff is zero. An example of a zero sum game is a game of rock paper scissors.
- A game of rock paper scissors involves the players to make three hand gestures: a rock, paper and scissors. Rock beats scissors, scissors beat paper, and paper beats rock. If the gestures are the same, the game is tied. The following table shows the payoff matrix of a game of Rock Paper Scissors.
Complete Information
The concept of complete information is that each of the players know all the optimal strategies and payoffs of the other player.
Equilibrium Point
Equilibrium point, or called Nash equilibrium point, is a point such that each player has chosen the optimal selection given the decision of the other players.
