Non-cooperative game in the context of "Nash equilibrium"

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⭐ Core Definition: Non-cooperative game

In game theory, a non-cooperative game is a game in which there are no external rules or binding agreements that enforce the cooperation of the players. A non-cooperative game is typically used to model a competitive environment. This is stated in various accounts most prominent being John Nash's 1951 paper in the journal Annals of Mathematics.

Counterintuitively, non-cooperative game models can be used to model cooperation as well, and vice versa, cooperative game theory can be used to model competition. Some examples of this would be the use of non-cooperative game models in determining the stability and sustainability of cartels and coalitions.

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👉 Non-cooperative game in the context of Nash equilibrium

In game theory, a Nash equilibrium is a situation where no player could gain more by changing their own strategy (holding all other players' strategies fixed) in a game. Nash equilibrium is the most commonly used solution concept for non-cooperative games.

If each player has chosen a strategy – an action plan based on what has happened so far in the game – and no one can increase one's own expected payoff by changing one's strategy while the other players keep theirs unchanged, then the current set of strategy choices constitutes a Nash equilibrium.

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Non-cooperative game in the context of Cooperative game theory

In game theory, a cooperative or coalitional game is a game with groups of players who form binding "coalitions" with external enforcement of cooperative behavior (e.g. through contract law). This is different from non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing (e.g. through credible threats).

Cooperative games are analysed by focusing on coalitions that can be formed, and the joint actions that groups can take and the resulting collective payoffs.

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← Cooperative game theory ← Nash equilibrium
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Game theory → John Forbes Nash Jr. → Annals of Mathematics → Cooperative game theory →