Game Theory

Nash Bargaining Solution – Game Theory Tuesdays (3/1/16)

• disagreement point (also known as a threat point) which is a payoff level in case no agreement is reached (FWC: e.g. 0-0). Each party also has a utility function for how the party feels about an outcome.
• Which point should they agree upon? Nash suggested there are a few reasonable rules that should apply to the bargaining. Then he proved something remarkable: there will always be a solution, and the solution will be unique! The solution is also relatively easy to calculate: the outcome is the point that maximizes the product of the two players utility over their disagreement point.
• Now suppose Alice is risk averse and values money according to the square root of x while Bob’s is risk neutral and values money linearly as y. By Pareto efficiency, the two will get c and 1 – c. The Nash bargaining solution maximizes the product (√c)(1 – c), and it gives 1/3 to Alice and 2/3 to Bob. Simply because Alice is risk averse she gets half as much as Bob in the solution.