Superadditivity

Definition

Superadditivity refers to a property of cooperative games where the value of a coalition of players is greater than or equal to the sum of the values of its individual members. This means that when players work together in a coalition, they can achieve outcomes that are more beneficial than if they acted separately. It emphasizes the idea that collaboration leads to increased total value, highlighting the advantages of cooperation among players.

5 Must Know Facts For Your Next Test

1. Superadditivity ensures that if players form a coalition, their collective potential gain is maximized beyond their individual contributions.
2. In superadditive games, forming larger coalitions is often more beneficial, leading to strategic alliances among players.
3. The existence of superadditivity is critical for ensuring that cooperation is desirable and leads to better outcomes for all involved parties.
4. A simple example of superadditivity can be seen in joint ventures, where companies pool resources to create more value than they could independently.
5. Superadditivity plays a crucial role in determining stable allocations within the core, as it helps ensure that all members are better off by cooperating rather than acting alone.

Review Questions

• How does superadditivity impact the formation of coalitions in cooperative games?
  • Superadditivity encourages players to form coalitions because it ensures that the total value generated by collaborating will be greater than the sum of what each player could achieve alone. This principle motivates individuals to come together, fostering strategic alliances that can lead to enhanced benefits. Players recognize that cooperation allows them to access larger rewards and improve their overall outcomes compared to acting independently.
• Discuss how the characteristic function relates to the concept of superadditivity in cooperative games.
  • The characteristic function plays a key role in defining the values associated with different coalitions, and it must exhibit superadditivity for cooperation to be advantageous. When the characteristic function indicates that the value of a coalition exceeds the sum of its individual members' values, it confirms that collaboration leads to increased benefits. This relationship helps determine optimal strategies for forming coalitions and achieving maximum payoff.
• Evaluate the implications of superadditivity on resource allocation strategies within the core of cooperative games.
  • Superadditivity has significant implications for resource allocation within the core because it guarantees that cooperative arrangements yield higher total value. This principle guides how resources are divided among coalition members while ensuring that no group prefers to break away and act independently. Consequently, understanding superadditivity helps identify stable allocations where all players are incentivized to remain in their coalitions, as they receive benefits that exceed their individual potential gains.

Related terms

Coalition: A coalition is a group of players that comes together to achieve a common goal, often sharing resources and benefits in cooperative games.

Characteristic Function:

The characteristic function assigns a value to each coalition, indicating the worth or benefit that the coalition can achieve through cooperation.

Core:

The core is a solution concept in cooperative game theory that represents allocations of resources where no subset of players would prefer to deviate from their assigned shares.