In economics, the main criteria by which one can distinguish between different market forms are: the number and size of producers and consumers on the market, the type of goods and services being traded, and the degree to which information can flow freely. The major market forms are:
Perfect competition, in which the market consists of a very large amount of firms producing product in the same domain.
Monopsony, when there is only one buyer in a market
These somewhat abstract concerns tend to determine some but not all details of a specific concrete market system where buyers and sellers actually meet and commit to trade.
Beyond the normal utility maximizing agents, the efficient market hypothesis requires the agents have rational expectations; that on average the population is correct (even if no one person is) and whenever new relevant information appears, the agents update their expectations appropriately.
Another observed discrepancy between the theory and real markets is that at market extremes what fundamentalists might consider irrational behaviour is the norm: in the late stages of a bull market, the market is driven by buyers who take little notice of underlying value.
The market's ability to efficiently respond to a short term and widely publicized event such as a takeover announcement cannot necessarily be taken as indicative of a market efficient at pricing regarding more long term and amorphous factors however.