A.3 ProofsA.3.1 Proof of Lemma 1Follows from the discussion preceding the proposition.A.3.2 Proof of Lemma 2Follows from the observations that precede the lemma.A.3.3 Proof of Lemma 3ACD Regime. We start by deriving the conditions under which the active connecteddealers (ACD) regime obtains. In this equilibrium, a connected seller’s offer is accepted ifand only if the seller is matched with an unconnected buyer. This event has probabilityλπb, so that: