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This paper explores the extent to which the incompleteness of contracts can be attributed to their formal nature: the form, usually written, that contracts are required to take to be enforceable in a court of law by legal prescription, common practice, or simply the contracting parties' will. We model the formal nature of state-contingent contracts as the requirement that the mapping from states of the world to the corresponding outcomes must be of an algorithmic nature. It is shown that such algorithmic nature, although by itself is not enough to generate incomplete contracts, when paired with a similar restriction on the contracting parties' selection process yields endogenously incomplete optimal contracts.
Anderlini et al. (Tue,) studied this question.