A normal game consists of a certain number of players and a set of moves, with that players have certain payoffs for a each combination of strategies. Most cooperative games are presented in the function form, while the extensive and the normal forms are used for non cooperative games.
Extensive form can be used to put games in an order of play, games are often presented as trees (picture to the bottom) The player is specified by a number listed by the vertex. The lines coming out of the vertex represent a possible action or move for that player. The payoffs or what the player gets in return for that move are specified at the bottom of the tree. Player 1 would choose either move U or move D, and depending on that the other player choose, either U or D depending on player 1’s move. These are the way basic noncooperative games are played.
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Player 2 chooses Left 
Player 2 chooses Right 

Player 1 chooses Up 
4, 3  –1, –1 
Player 1 chooses Down 
0, 0  3, 4 
The normal (or strategic form) game is usually represented by a matrix which shows the players, strategies, and payoffs (see the example to the right). In this example there are two platers. One of the players chooses 1 row and the other chooses the column. Along with this each player has strategies, which are showed be the number or rows and columns. The payoffs are provided in the interior. The first number is the payoff that the first player gets (Player 1 in the example) The second is the payoff for the column player (Player 2 in the example). As an example Player 1 plays Up and that Player 2 plays Left. Then Player 1 gets a payoff of 4, and Player 2 gets 3.
In cooperative games with “transferable utility” no individual payoffs are given because both players are working together for an equal goal. Instead, the characteristic function determines the payoff of each coalition. The standard assumption is that the empty coalition obtains a payoff of 0.