Cooperative Games Summary

Game Theory · Axiom Academy

SUMMARY Cooperative Games Summary Unit 6 - Cooperative Game Theory: Key Concepts Review Cooperative vs Non-Cooperative Games Non-Cooperative Games: Players act independently, pursuing individual strategies. Focus is on Nash equilibria and strategic interactions (Units 1-5) Cooperative Games: Players can form binding coalitions and negotiate agreements. Focus shifts to group value and fair distribution Key Difference: Cooperation allows players to commit to joint strategies and share collective payoffs Binding Agreements: Coalition members can enforce commitments, unlike non-cooperative settings Characteristic Function & Coalitions Coalition: A subset S ⊆ N of players who agree to work together Characteristic Function: v(S) assigns a value to each coalition, representing what they can guarantee themselves Superadditivity: For disjoint coalitions, v(S ∪ T) ≥ v(S) + v(T) means cooperation doesn't hurt Grand Coalition: All players together ( N ) typically maximizes total value Imputation: A payoff vector x = (x₁, x₂, ..., xₙ) that divides the grand coalition's value among players Efficiency: ∑ xᵢ = v(N) ensures all value is distributed (no waste) Individual Rationality: xᵢ ≥ v( i ) ensures each player gets at least their stand-alone value Fairness Criteria: Different solution concepts balance efficiency with equitable distribution The Core: Set of imputations where no coalition has incentive to deviate Core Condition: For all S ⊆ N : ∑ i∈S xᵢ ≥ v(S)

This is the written version of the interactive lesson above. See the full Game Theory course.