Nash bargaining solution (1950): given a compact convex feasible set S and disagreement point d, the unique solution satisfying Pareto efficiency, symmetry, scale invariance, and independence of irrelevant alternatives (IIA) maximizes the Nash product: N(u) = (u₁−d₁)^α₁ · (u₂−d₂)^(1−α₁).
Geometric construction: the solution is the tangency of a hyperbola (u₁−d₁)(u₂−d₂) = const with the frontier. For asymmetric Nash bargaining with power α₁, the solution gives player 1 fraction α₁ of the surplus above d. Applications: wage negotiation, trade agreements, divorce settlements.