Nash's Bargaining Problem (1950)
Just before John Nash made his breakthrough discovery of the Nash equilibrium, he wrote his first paper on another problem later to be known as Nash’s bargaining game. Nash’s bargaining game is a study of cooperative bargaining and the demonstration of a unique solution to a two-person bargaining problem (Nash, 1950). Stated simply, the setup for the bargining problem is as follows:
Two players demand a portion of some good (usually some amount of money). If the total amount requested by the players is less than that available, both players get their request. If their total request is greater than that available, neither gets their request.
Nash’s axiomatic approach proposes that a solution to the latter case must satisfy the axioms of:
Invariance (INV), such that a transformation of the utility function that maintains the same ordering over preferences should not alter the outcome of the bargaining process;
Weak Pareto efficiency (WPO), such that players never agree on an outcome s when …