Core

Definition

In game theory, the core refers to a set of feasible allocations that cannot be improved upon by any subset of players through their collective action. It represents outcomes where no group of players can gain by breaking away from the proposed allocation, highlighting stability in cooperative settings. The core connects with concepts like fairness and efficiency, as it seeks to ensure that resources are distributed in a way that all participants feel satisfied and no one has an incentive to deviate.

5 Must Know Facts For Your Next Test

1. The core is relevant in cooperative games, where players can negotiate binding agreements and share the outcomes.
2. An allocation is in the core if there are no groups of players who can find a more beneficial arrangement by splitting off and forming their own coalition.
3. The core can be empty in some situations, meaning that there are no allocations that satisfy all participants simultaneously.
4. Understanding the core helps in analyzing how stable agreements can be formed and maintained among individuals or groups.
5. The concept of the core is vital in ensuring fairness, as it strives for allocations where all parties have no reason to feel cheated or excluded.

Review Questions

• How does the concept of the core relate to stability in cooperative game scenarios?
  • The core represents allocations that maintain stability among players in cooperative games by ensuring that no subset of players has an incentive to break away for a better outcome. If an allocation lies within the core, it means that every player or coalition feels satisfied with the distribution and sees no advantage in departing from it. This stability is crucial for fostering cooperation and ensuring that agreements are upheld.
• Discuss the implications of an empty core for coalitions in a game setting.
  • An empty core indicates that there are no feasible allocations where all participants are satisfied, leading to potential instability within coalitions. Without an allocation in the core, groups may struggle to form because individuals or subsets may always find alternative arrangements that they perceive as better. This situation complicates negotiations and could lead to conflicts, as players seek out their own interests rather than working collectively.
• Evaluate how the concept of the core can be applied to real-world negotiations or resource distributions.
  • The core can be utilized in various real-world scenarios such as labor negotiations, international agreements, or resource-sharing arrangements where multiple parties must come to an agreement. By aiming for allocations within the core, negotiators can ensure that all involved parties are content with the outcome, reducing the likelihood of disputes and fostering cooperation. Understanding this concept helps stakeholders find solutions that recognize everyone's contributions and needs, leading to more sustainable agreements and stronger relationships.

Related terms

Nash Equilibrium: A situation in a game where no player can benefit by unilaterally changing their strategy while the other players keep theirs unchanged.

Shapley Value:

A solution concept that assigns a unique distribution of a total payoff among players based on their individual contributions to the coalition.

Coalition: A group of players that come together to coordinate their strategies and share the payoffs resulting from their collective actions.