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In cooperative game theory, the core is the set of feasible allocations or imputations where no coalition of agents can benefit by breaking away from the grand coalition. One can think of the core corresponding to situations where it is possible to sustain cooperation among all agents.
Cooperative game theory is a branch of game theory that deals with the study of games where players can form coalitions, cooperate with one another, and make binding agreements. The theory offers mathematical methods for analysing scenarios in which two or more players are required to make choices that will affect other players wellbeing. [5]
For 2-player games the set of imputations coincides with the core, a popularly studied concept due to its stability against group deviations. [2] The core is a solution concept of cooperative games and consists of multiple imputations, a set of distributions as a result of a game. The core cannot be improved upon by any coalition. [3]
In cooperative game theory, the Shapley value is a method (solution concept) for fairly distributing the total gains or costs among a group of players who have collaborated. For example, in a team project where each member contributed differently, the Shapley value provides a way to determine how much credit or blame each member deserves.
The Bondareva–Shapley theorem, in game theory, describes a necessary and sufficient condition for the non-emptiness of the core of a cooperative game in characteristic function form. Specifically, the game's core is non-empty if and only if the game is balanced.
Cooperative games are often analyzed through the framework of cooperative game theory, ... A core part of the imperfect information specification is the set of states ...
In cooperative game theory, the nucleolus of a cooperative game is the solution (i.e., allocation of payments to players) that maximizes the smallest excess of a coalition (where the excess is the difference between the payment given to the coalition and the value the coalition could get by deviating).
Cooperative game may refer to: Cooperative board game, board games in which players work together to achieve a common goal; Cooperative game theory, in game theory, a game with competition between groups of players and the possibility of cooperative behavior; Cooperative video game, a video game that allows players to work together as teammates