Cooperative Games in Game Theory
In cooperative games, players can form coalitions to achieve a common goal. The main difference between cooperative games and non-cooperative games is that the former allows players to communicate and cooperate with each other to achieve a shared objective. In contrast, non-cooperative games do not allow for such cooperation.
Let's take a simple example of a cooperative game. Imagine you and your friend are both trying to move a heavy object, but it's too heavy for either of you to move alone. However, if you both work together, you can easily move the object. In this scenario, you and your friend form a coalition to achieve a common goal, i.e., moving the heavy object.
Coalitional games are represented by a set of players, a characteristic function, and a payoff function. The characteristic function defines which coalitions are feasible and which are not. The payoff function specifies the payoffs of each coalition.
The main objective of cooperative game theory is to find the best way to distribute the payoff among the players. This is done by finding a cooperative solution, which is a set of payoff allocations that satisfies certain properties. Some of the most popular cooperative solutions are the core, the Shapley value and the Nash bargaining solution.
Overall, cooperative games are an important area of game theory that allows players to work together to achieve a common goal.
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