A Fictitious Play of the Nash Demand Game Implements the Nash Bargaining Solution

We study a repeated Nash demand game, where bargainers follow a fictitious play procedure after their one-shot decision on demand in the initial period. In the reduced static game they play at the initial period, all the epsilon-equilibria are clustered around the division corresponding to the Nash bargaining solution when the bargainers are patient. As the bargainers make a more accurate comparison of payoffs and become more patient accordingly, the only equilibrium left is the division of the Nash bargaining solution.