What is the difference between double auction and continuous double auction? Sometimes I feel that they were types of two-sided auction but sometimes I feel as if they were two separate concepts.
So, if a distinction is made, as continuous double auctions are usually just called double auctions, then the difference has to do with frequency. It is easier to have an example.
The New York Stock Exchange is an example of a continuous double auction. Within its trading hours, you can bid in either direction as much or as often as you want and so can everyone else.
The best example of an ordinary double auction was the Arizona Stock Exchange which closed in 2001. It only permitted two bids per day, at the open of US trading and at the close. It sought to solve an institutional liquidity problem. Certain types of institutions are at risk if they cannot clear their orders at or as near to as possible a particular moment in time. Mutual funds, for example, usually only have one valuation per day and if there need to be a lot of transactions from redemption or purchase activity, then the least risk is to have the trade near that time. Most are at the open or close.
The Arizona exchange found the single price that cleared the largest number of trades. You paid a fee to participate. There was no bid-ask spread. So possibly hundreds of customers would place their limit orders at the same time as buyers or sellers. What they did in practice was create single supply curve and a single demand curve and the price paid/received was the intersection of the two curves.