Game Theory – Module 4

Cooperative Game Theory

Shapley Value • Core • Nash Bargaining Solution • Nucleolus

Define Game

Example 1 – Production Coalition
3 firms can produce alone or jointly. Coalitions create synergies (economies of scale). Who gets which share?
3 players · Shapley · Core
Example 2 – Voting Weights
4 parties with different voting weights. Who actually has the most power? (Shapley power index)
4 players · Power index · Weighted game
Example 3 – Cost Sharing
3 cities share infrastructure costs. The Shapley value determines the fair cost contribution for each city.
3 players · Cost game · fair allocation
Player names: optionally editable.   v(S): Value of coalition S (what S can jointly achieve). v(∅) = 0 always. Singleton v({i}) = standalone value.

Coalition Values v(S)