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Weak Core
In cooperative game theory, the core is the Set (mathematics), set of Feasible region, feasible allocations or Imputation (game theory), imputations where no coalition of agents can benefit by breaking away from the grand coalition. An allocation is said to be in the ''core'' of a game if there is no coalition that can improve upon it. The core is then the set of all feasible allocations. Origin The idea of the core already appeared in the writings of , at the time referred to as the ''contract curve''. Even though John von Neumann, von Neumann and Oskar Morgenstern, Morgenstern considered it an interesting concept, they only worked with zero-sum games where the core is always Empty set, empty. The modern definition of the core is due to Donald B. Gillies, Gillies. Definition Consider a transferable utility Cooperative game theory, cooperative game (N,v) where N denotes the set of players and v is the Game theory#Characteristic function form, characteristic function. An Imputati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooperative Game Theory
In game theory, a cooperative game (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. Mathematical definition A cooperative game is given by specifying a value for every coalition. Formally, the coalitional game consists of a finite set of players N , called the ''grand coalition'', and a ''characteristic function'' v : 2^N \to \mathbb from the set of all possible coalitions of players to a set of payments that satisfies v( \emptyset ) = 0 . The function describes how much collective payoff a set of players can gain by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |