key term - Cooperative Game

Definition

A cooperative game is a type of game in game theory where players can form binding commitments and work together to achieve better outcomes than they could individually. These games focus on how players can benefit from cooperating, and they often lead to negotiations on resource allocation, profit sharing, or strategy development, emphasizing the importance of collaboration over competition.

5 Must Know Facts For Your Next Test

1. In cooperative games, players can negotiate and form coalitions to improve their outcomes, leading to mutual benefits.
2. The core of a cooperative game represents allocations where no subset of players would prefer to break away and form their own coalition.
3. Cooperative games can often be represented by characteristic functions that specify the value of each possible coalition.
4. The Shapley Value provides a method to fairly distribute the total gains among players based on their contributions to various coalitions.
5. Examples of cooperative games include business partnerships, joint ventures, and international treaties where collaboration is essential for success.

Review Questions

• How do players in a cooperative game benefit from forming coalitions, and what factors influence the formation of these coalitions?
  • Players in a cooperative game benefit from forming coalitions as they can achieve outcomes that are more favorable than those possible through individual play. Factors influencing coalition formation include shared interests, trust among players, and the potential for increased payoffs. By working together, players can negotiate resource allocation and strategize effectively, thus maximizing their overall utility.
• Discuss the significance of the core in cooperative games and how it relates to players' motivations in forming coalitions.
  • The core is significant in cooperative games as it represents allocations where no subset of players would prefer to deviate from the proposed distribution to form their own coalition. This reflects the motivations behind coalition formation: players seek outcomes that ensure stability and fairness. If an allocation falls within the core, it encourages cooperation as all parties feel adequately rewarded without risking loss by breaking away.
• Evaluate how the Shapley Value provides a solution for fairly distributing gains in cooperative games and its implications for real-world applications like business partnerships.
  • The Shapley Value evaluates each player's contribution to various coalitions and assigns them a fair share of total gains based on their impact. This method is crucial for resolving disputes over profit sharing in real-world applications such as business partnerships, ensuring that rewards are allocated according to each participant's actual contribution. By promoting fairness, the Shapley Value fosters cooperation and trust among players, which is essential for long-term collaborative efforts.

Related terms

Coalition: A group of players in a cooperative game who come together to achieve a common goal, sharing the benefits of their collaboration.

Core:

A concept in cooperative games representing the set of feasible allocations of resources that cannot be improved upon by any coalition of players.

Shapley Value:

A solution concept in cooperative game theory that assigns a unique distribution of total gains to players based on their individual contributions to the coalition.