We investigate the relationship between the inner core and asymmetric Nash

bargaining solutions for n-person bargaining games with complete information. We

show that the set of asymmetric Nash bargaining solutions for different strictly

positive vectors of weights coincides with the inner core if all points in the underlying

bargaining set are strictly positive. Furthermore, we prove that every bargaining

game is a market game. By using the results of Qin (1993) we conclude that for

every possible vector of weights of the asymmetric Nash bargaining solution there

exists an economy that has this asymmetric Nash bargaining solution as its unique

competitive payoff vector. We relate the literature of Trockel (1996, 2005) with

the ideas of Qin (1993). Our result can be seen as a market foundation for every

asymmetric Nash bargaining solution in analogy to the results on non-cooperative

foundations of cooperative games.