Cooperative Games in Game Theory
In game theory, two main types of games are Non-Cooperative and Cooperative games.
In a non-cooperative game, players make their decisions independently of each other, whereas in cooperative games, players cooperate with each other to achieve a common goal. In non-cooperative games, players are assumed to be selfish and rational, and they aim to maximize their own payoffs. Non-cooperative games are usually represented as strategic-form games or extensive-form games. In strategic-form games, players choose their strategies simultaneously, whereas in extensive-form games, players take turns to make decisions, and the game is represented as a decision tree. Players can use various solution concepts to predict the outcome of the game. The most popular solution concept is the Nash equilibrium, which is a set of strategies, one for each player, such that no player can improve their payoff by unilaterally changing their strategy.
In contrast, cooperative games are characterized by the formation of coalitions among players, who share their payoffs among themselves. Cooperative games are represented as characteristic function games. Cooperative games have several solution concepts that take into account the formation of coalitions among players. Some of the popular solution concepts in cooperative games are the core solution, the Shapley value, and the Nash bargaining solution.
An example of a non-cooperative game is the Prisoner's dilemma, where two suspects are interrogated separately, and each has to decide whether to cooperate with the other or betray them. If both suspects cooperate, they both receive a light sentence, whereas if both betray each other, they both receive a heavy sentence. If one betrays the other and the other cooperates, the betrayer goes free, and the other receives a heavy sentence. In contrast, an example of a cooperative game is the allocation of a budget among different departments of a company. The departments have to cooperate to determine how to allocate the budget, and they share the benefits according to some criterion, such as their contribution to the company's revenue.
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