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The union of any finite collection of corners is the attainable set of a market with continuous, monotone increasing, quasiconcave utility functions. It follows that the attainable sets of such markets are dense in the collection of attainable sets of markets with utility functions restricted only to being upper-semicontinuous and lower-bounded. One approach to the study of an economic market is to construct a cooperative «-person game from the market (9), (10). Game-theoretic analysis then yields results which can be interpreted in the context of the original market. It is, therefore, of interest to characterize those games which can arise from markets of various kinds. Shapley and Shubik (10) considered markets in which utility is linearly transferable between traders. They showed that the corresponding (side-payment) games are precisely those which are totally balanced. Similar results are known for markets in which all traders have concave utility functions (3), (4), (8). The situation for more general markets is less settled. A natural starting point is to determine which sets of possible outcomes are associated with markets in which all traders have well-behaved utility func- tions. It is our purpose to investigate the character of these sets when the utility functions are restricted to being continuous, monotone increasing, and quasiconcave. We will find that these sets are dense in the collection of sets associated with markets in which the traders' utility functions are much less well behaved.

Attainable sets of quasiconcave markets