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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]
Consider a transferable utility cooperative game (,) where denotes the set of players and is the characteristic function.An imputation is dominated by another imputation if there exists a coalition , such that each player in weakly-prefers (for all ) and there exists that strictly-prefers (<), and can enforce by threatening to leave the grand coalition to form (()).
Nash's most famous contribution to game theory is the concept of the Nash equilibrium, which is a solution concept for non-cooperative games, published in 1951. A Nash equilibrium is a set of strategies, one for each player, such that no player can improve their payoff by unilaterally changing their strategy.
Solutions in non-cooperative games are similar to all other games in game theory, but without the ones involved binding agreements enforced by the external authority. The solutions are normally based on the concept of Nash equilibrium , and these solutions are reached by using methods listed in Solution concept .
If the cooperative game is given by enumerating all coalitions' values, then the input size is 2 n, and so the above algorithms run in time polynomial in the input size. But when n is large, even representing such a game is computationally intensive, and there is more interest in classes of cooperative games that have a compact representation.
Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.
An important problem in the theory of cooperative dynamic games is the time-consistency of a given imputation function (in Russian literature it is termed dynamic stability of optimality principle). Let say that a number of players has made a cooperative agreement at the start of the game.
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