The games studied by game theory are well-defined mathematical objects. A game consists of a set of players, a set of moves (or strategies) available to those players, and a specification of payoffs for each combination of strategies. There are two ways of representing games that are common in the literature.
Normal form
| Player 2 chooses left | Player 2 chooses right | |
|---|---|---|
| Player 1 chooses top | 4, 3 | -1, -1 |
| Player 1 chooses bottom | 0, 0 | 3, 4 |
The normal (or strategic form) game is a matrix which shows the players, strategies, and payoffs (see the example to the right). Here there are two players; one chooses the row and the other chooses the column. Each player has two strategies, which are specified by the number of rows and the number of columns. The payoffs are provided in the interior. The first number is the payoff received by the row player (Player 1 in our example); the second is the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays top and that Player 2 plays left. Then Player 1 gets 4, and Player 2 gets 3.
When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other. If players have some information about the choices of other players, the game is usually presented in extensive form.
Extensive form
Extensive form games attempt to capture games with some important order. Games here are presented as trees (as pictured to the left). Here each vertex (or node) represents a point of choice for a player. The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action for that player. The payoffs are specified at the bottom of the tree.
In the game pictured here, there are two players. Player 1 moves first and chooses either F or U. Player 2 sees Player 1′s move and then chooses A or R. Suppose that Player 1 chooses U and then Player 2 chooses A, then Player 1 gets 8 and Player 2 gets 2.
Extensive form games can also capture simultaneous-move games as well. Either a dotted line or circle is drawn around two different vertices to represent them as being part of the same information set (i.e., the players do not know at which point they are).
This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.
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