In game theory, a non-cooperative game is a game with competition between individual players, as opposed to cooperative games, and in which alliances can only operate if self-enforcing (e.g. through credible threats). However, 'cooperative' and 'non-cooperative' are only technical terms to describe the theory used to model a game, so it is possible to use cooperative game theory to model competition and using non-cooperative game theory to model cooperation. The key distinguishing feature is the absence of external authority to establish rules enforcing cooperative behavior. In the absence of external authority (such as contract law), players cannot group into coalitions and must compete independently. Negative-sum games and zero-sum games are both types of non-cooperative games. Non-cooperative game theory in academic literature A mention of non-cooperative game theory was made in John Nash's 1951 article in the journal Annals of Mathematics. Nash Equilibrium, in fact, are often referred to as "non-cooperative equilibrium". According to Tamer Başar in Lecture Notes on Non-Cooperative Game Theory, a non-cooperative game requires specifying: the number of players; the possible actions available to each player, and any constraints that may be imposed on them; the objective function of each player which he or she attempts to optimise; any time ordering of the execution of the actions if the players are allowed to act more than once; any information acquisition that takes place and how the information available to a player at each point in time depends on the past actions of other players, and; whether there is a player (nature) whose action is the outcome of a probabilistic event with a fixed (known) distribution. Assumptions Perfect recall: each player remembers his/ her decisions and knowned information. Self-interest: each player does not consider the effect of actions on the others but only on his/ her own. Rational: each player is interested to maximise his/ her utility or payoff. Complete information: each player knows the preferences and strategies of the other players. Each player has the same understanding of how the game is. Analysis 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. This framework often requires a detailed knowledge in the possible actions and the levels of information of each player. It is opposed to cooperative game theory, which focuses on predicting which groups of players ("coalitions") will form, the joint