We consider the inner core as a solution concept for cooperative games with non-

transferable utility (NTU) and its relationship to competitive equilibria of markets

that are induced by an NTU game. We investigate the relationship between certain

subsets of the inner core for NTU market games and competitive payoff vectors of

markets linked to the NTU market game. This can be considered as the case in

between the two extreme cases of Qin (1993). We extend the results of Qin (1993)

to a large class of closed subsets of the inner core: Given an NTU market game

we construct a market depending on a given closed subset of its inner core. This

market represents the game and further has the given set as the set of payoffs of

competitive equilibria. It turns out that this market is not determined uniquely and

thus we obtain a class of markets with the desired property.