Market Design by Guillaume Haeringer

Author:Guillaume Haeringer [Haeringer, Guillaume]
Language: eng
Format: epub

d ∈ S, meaning doctor d (Dr. Alice in our example), is in the group, and

d′ ∉ S, meaning doctor d′ (Dr. Bob in our example), is not in the group,

then we have

Here the notation S ∪{d′}\{d} means that we take the group of doctors S where we add doctor d′ (the notation ∪{d′}) and we withdraw doctor d (the notation \{d}).

We illustrate how responsive preferences work in the following example.

Example 10.1   We consider a hospital, called hospital h, and four doctors, called d1, d2, d3, and d4. What is given to construct responsive preferences (and we have seen that this is enough) are the preferences over doctors, Ph. Let us assume that hospital h’s preferences over these four doctors are

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