Cooperative game theory


In game theory, a cooperative game or coalitional game is a game with competition between groups of players "coalitions" due to the possibility of outside enforcement of cooperative behavior e.g. through contract law. Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or any agreements need to be self-enforcing e.g. through credible threats.

Cooperative games are often analysed through the model of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups draw and the resulting collective payoffs. it is for opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions together with payoffs as living as analyzing Nash equilibria.

Cooperative game theory enables a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperative game conviction also looks at how bargaining procedures will impact the distribution of payoffs within regarded and identified separately. coalition. As non-cooperative game abstraction is more general, cooperative games can be analyzed through the approach of non-cooperative game theory the converse does not score provided that sufficient assumptions are delivered to encompass any the possible strategies usable to players due to the possibility of external enforcement of cooperation. While it would thus be possible to have all games expressed under a non-cooperative framework, in many instances insufficient information is available to accurately advantage example the formal procedures available to the players during the strategic bargaining process, or the resulting model would be of too high complexity to advertising a practical tool in the real world. In such(a) cases, cooperative game theory authorises a simplified approach that allows the analysis of the game at large without having to make any condition about bargaining powers.

Relation with non-cooperative theory


Let G be a strategic non-cooperative game. Then, assuming that coalitions have the ability to enforce coordinated behaviour, there are several cooperative games associated with G. These games are often indicated to as representations of G. The two specifications representations are: