In game theory, a non-cooperative game is a game with competition between individual players and in which only self-enforcing (e.g. through credible threats) alliances (or competition between groups of players, called "coalitions") are possible due to the absence of external means to enforce cooperative behavior (e.g. contract law), as opposed to cooperative games.
The key feature of a non-cooperative game is the absence of an external authority to enforce rules.
Non-cooperative games are generally analysed through the framework of non-cooperative game theory, which tries to predict players' individual strategies and payoffs and to find Nash equilibria.  It is opposed to cooperative game theory which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs and does not analyze the strategic bargaining that occurs within each coalition and affects the distribution of payoffs between members of a same coalition.
Non-cooperative game theory provides a low-level approach as it models all the procedural details of the game, whereas cooperative game theory only describes the structure, strategies and payoffs of coalitions. Non-cooperative game theory is in this sense more inclusive than cooperative game theory.
It is also more general, as cooperative games can be analyzed using the terms of non-cooperative game theory. Where arbitration is available to enforce an agreement, that agreement falls outside the scope of non-cooperative theory: but it may be possible to state sufficient assumptions to encompass all the possible strategies players may adopt, in relation to arbitration. This will bring the agreement within the scope of non-cooperative theory. Alternatively, it may be possible to describe the arbitrator as a party to the agreement and model the relevant processes and payoffs suitably.
Accordingly, it would be desirable to have all games expressed under a non-cooperative framework. But in many instances insufficient information is available to accurately model the formal procedures available to the players during the strategic bargaining process; or the resulting model would be of too high complexity to offer a practical tool in the real world. In such cases, cooperative game theory provides a simplified approach that allows analysis of the game at large without having to make any assumption about bargaining powers.