Bargaining problem

The two-person bargaining problem is a problem of understanding how two agents should cooperate when non-cooperation leads to Pareto-inefficient results. It is in essence an equilibrium selection problem; many games have multiple equilibria with varying payoffs for each player, forcing the players to negotiate on which equilibrium to target. Solutions to bargaining come in two flavors: an axiomatic approach where desired properties of a solution are satisfied and a strategic approach where the bargaining procedure is modeled in detail as a sequential game.

The bargaining game

The bargaining game or Nash bargaining game is a simple two-player game used to model bargaining interactions. In the Nash bargaining game, 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 player gets their request. A Nash bargaining solution is a Pareto efficient solution to a Nash bargaining game. According to Walker, Nash's bargaining solution was shown by John Harsanyi to be the same as Zeuthen's solution of the bargaining problem.