If the parties to an agreement could specify their respective rights and duties for every possible future state of the world, their contract would be complete.
The idea of a complete contract is closely related to the notion of default rules, e.g. legal rules that will fill the gap in a contract in the absence of an agreed upon provision.
In the presence of asymmetric information, the optimization problems can be handled due to the revelation principle.
A leading textbook exposition of complete contract theory is Laffont and Martimort (2002).
[2] In contrast, incomplete contracting models consider situations in which only a restricted class of contracts is allowed, e.g. only simple ownership structures can be contractually specified in the Grossman-Hart-Moore theory of the firm.