“…First, we define full substitutability in the language of choices, adapting and merging the Ostrovsky () same‐side substitutability and cross‐side complementarity conditions. Setting conditions on how each agent's optimal choice changes as that agent's opportunity set expands originated in the matching literature, where it is natural to consider an expansion in the set of available trades and, thus, an expansion in the set of available contracts (see Ostrovsky 2008, Westkamp 2010, Hatfield and Kominers 2012, Hatfield et al 2013, and Hatfield, Kominers, and Westkamp 2019). In choice language, we say that a choice correspondence is fully substitutable if, when attention is restricted to sets of contracts for which is single‐valued, whenever the set of options available to i on one side expands, i rejects a larger set of contracts on that side (same‐side substitutability) and selects a larger set of contracts on the other side (cross‐side complementarity).…”