Cooperative games are a type of game in which players work together to achieve a common goal. In contrast to non-cooperative games, where players act independently of one another, cooperative games require collaboration and coordination.

Coalition

One of the key concepts in cooperative games is the notion of a coalition. A coalition is a group of players who work together towards a common goal. The value of a coalition is the amount that its members can achieve by working together. For example, in a game where the players are competing for a fixed amount of money, a coalition that includes all of the players will receive the entire prize.

There are different ways to distribute the value of a coalition among its members. One common method is the Shapley value, which is based on the idea of marginal contributions. The Shapley value assigns to each player the average marginal contribution of that player across all possible coalitions. This ensures that each player is rewarded for their contributions to the coalition, but not more than what they deserve.

Core

Another important concept in cooperative games is the core. The core is the set of outcomes that are stable and cannot be improved upon by any coalition. In other words, no group of players can gain more by forming a coalition and deviating from the core outcome. The core provides a way to identify fair and stable outcomes in cooperative games.

Examples of cooperative games include the prisoner's dilemma, where two players must cooperate to avoid a worse outcome, and the tragedy of the commons, where multiple players must work together to avoid depleting a shared resource.

All courses were automatically generated using OpenAI's GPT-3. Your feedback helps us improve as we cannot manually review every course. Thank you!