Non-cooperative game theory

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).

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.

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. It is opposed to cooperative game theory, which focuses on predicting which groups of players ("coalitions") will form, the joint actions that groups will take, and the resulting collective payoffs. Cooperative game theory does not analyze the strategic bargaining that occurs within each coalition and affects the distribution of the collective payoff between the members.

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.

See also

• Assured destruction
• Grim trigger
• Intra-household bargaining
• Nash equilibrium
• Proper equilibrium
• Tit for tat
• Trembling hand perfect equilibrium
• Trigger strategy
• War of attrition (game)
• Zero-sum game

External links

• A brief introduction to non-cooperative game theory
• An Introductory Course in Noncooperative Game Theory (requires password)