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This chapter standardizes terminology, places the double auction (DA) institution and its variants in the taxonomy of market institutions, and distinguishes the different sorts of trading environments. It surveys several strands of the theoretical literature relevant to the DA. Many variants of the basic continuous DA have been employed in field and laboratory environments. At the University of Arizona, work is also underway on a series of hybrid institutions which feature a "price clock" reminiscent of the clock used in Dutch flower auctions. Perhaps the most natural way for a modern theorist to think about a market institution is as a game of incomplete information, since traders generally do not know each others' preferences. Models of trading institutions as games of incomplete information have dominated the theoretical literature, but there are alternative approaches. The chapter also surveys some of the relevant empirical literature.
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