Cooperative game

Definition

A cooperative game is a type of game in game theory where players can negotiate and form binding commitments to work together to achieve mutual benefits. This contrasts with non-cooperative games, where players make decisions independently. Cooperative games focus on the collective strategies of the players, emphasizing collaboration and shared payoffs rather than individual actions.

5 Must Know Facts For Your Next Test

1. In cooperative games, players can form alliances or coalitions to improve their overall payoff compared to playing independently.
2. The Shapley value is a key concept used to fairly allocate the total gains from cooperation among players based on their contributions.
3. Cooperative games can be analyzed using different solution concepts, including the core, the Shapley value, and the Nash bargaining solution.
4. An essential aspect of cooperative games is that binding agreements are possible, allowing players to commit to strategies that benefit all members of a coalition.
5. Applications of cooperative game theory are common in areas like business negotiations, joint ventures, and resource allocation where collaboration leads to better outcomes.

Review Questions

• How does the concept of a cooperative game differ from that of a non-cooperative game in terms of player interactions?
  • In a cooperative game, players interact by forming coalitions and making binding agreements to work together for mutual benefits. This contrasts with non-cooperative games, where players act independently and cannot form enforceable commitments. The ability to collaborate in cooperative games allows for collective strategies that often lead to improved payoffs compared to the competitive nature of non-cooperative scenarios.
• Discuss the significance of the Shapley value in cooperative games and how it influences player decision-making.
  • The Shapley value is crucial in cooperative games as it provides a method for fairly distributing the total payoff among players based on their contributions to the coalition. This concept encourages players to participate in cooperation since they know their input will be rewarded fairly. By establishing an equitable distribution, the Shapley value helps sustain long-term collaborations and reduces conflicts over resource allocation among coalition members.
• Evaluate how cooperative game theory can be applied in business strategy and what implications it has for competitive markets.
  • Cooperative game theory offers valuable insights into business strategy by highlighting how companies can form partnerships or alliances to enhance their market positions. For example, firms may collaborate on research and development or share resources to lower costs and increase innovation. This approach can lead to more efficient outcomes than competing independently. However, companies must also navigate potential conflicts that arise when determining how to distribute benefits from cooperation, influencing competitive dynamics in markets.

Related terms

Nash Bargaining Solution:

A solution concept in cooperative game theory that determines how to fairly distribute payoffs among players who can negotiate their agreements.

Coalition: A group of players that come together to form a partnership in a cooperative game to achieve better outcomes than they could individually.

Core:

A set of outcomes in a cooperative game where no coalition of players would prefer to deviate from the proposed distribution because they cannot achieve a better payoff.