We develop a model of information processing and strategy choice for participants in a double auction. Sellers in this model form beliefs that an offer will be accepted by some buyer. Similarly, buyers form beliefs that a bid will be accepted. These beliefs are formed on the basis of observed market data, including frequencies of asks, bids, accepted asks, and accepted bids. Then traders choose an action that maximizes their own expected surplus. The trading activity resulting from these beliefs and strategies is sufficient to achieve transaction prices at competitive equilibrium and complete market efficiency after several periods of trading.