Bargaining Games

Game Theory · Axiom Academy

Understanding how rational agents divide resources through cooperative negotiation 1. The Bargaining Problem Setup A two-person bargaining problem consists of: Two players who can cooperate to achieve joint outcomes A feasible set of possible utility pairs they can achieve together A disagreement point representing what each player gets if negotiation fails The animation below shows how players start at the disagreement point and negotiate toward outcomes in the feasible set. 2. The Feasible Set and Pareto Frontier The feasible set S represents all utility pairs (u₁, u₂) the players can achieve through cooperation. Not all points are equally desirable: Pareto efficient points lie on the frontier - no player can improve without hurting the other Dominated points lie in the interior - both players prefer moving to the frontier A good bargaining solution must select a Pareto efficient outcome. 3. Properties of Good Bargaining Solutions A bargaining solution f maps each bargaining problem (S, d) to a point in S. Desirable properties include: Pareto Efficiency: Select a point on the frontier Individual Rationality: Each player gets at least their disagreement payoff Symmetry: Identical players receive identical payoffs Independence of Irrelevant Alternatives: If the solution remains feasible when options are removed, it shouldn't change 4. The Nash Bargaining Solution

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