We provide a new interpretation of the Nash solution. The "Nash" solution can be interpreted as the "Nash" equilibrium of a version of the "Nash" demand game, which is based on the fictitious play process. Based on our finding that the Nash demand game has the fictitious play property almost everywhere, we show that the game which determines the initial demands of the fictitious play process approximately implements the Nash solution. We show furthermore that the Nash division is the only epsilon-equilibrium surviving as the players make a more accurate comparison of payoffs and become more patient accordingly. We also show that the Nash division is the unique Nash equilibrium of the initial demand game when we use the limit of average payoffs to rank the payoff sequences.