Non-cooperative game
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A non-cooperative game, in opposition of a cooperative game, players make decisions independently. Thus, while players could cooperate, any cooperation must be self-enforcing. A game in which players can enforce contracts through third parties is a cooperative game.
The non-cooperative games can be sequential or not. Both can be represented by a extended form (decision tree), but only the non-sequential can be represented as a bimatrix of payoffs.