The competitive outcomes of an economic system are known, under quite general conditions, always to lie in the core of the associated cooperative game. It is shown here that every market game (i.e., one that arises from an exchange economy with money) can be represented by a direct market whose competitive outcomes completely fill the core. It is also shown that it can be represented by a market having any given core outcome as its unique competitive outcome, or, more generally, having any given compact convex subset of the core as its full set of competitive outcomes.
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