Online Appendix for A Pooling Analysis of Two Simultaneous Online Auctions

This section provides theoretical support for the strategy outlined in §2.2. For convenience, to ease the presentation of the case in which auctioneer a’s reservation price is not met, we imagine there arema+1 “reservation” dedicated bidders installed in auction a at the market’s outset, where each such bidder’s valuation equals auctioneer a’s reservation price. Thus in this section of the appendix we assume without loss of generality that da ≥ ma+1, a = 1, 2. See §2.1 for informational assumptions. Note that the equilibrium analysis presented below generalizes the model from the main text, by allowing for non-identically distributed bidder valuations. Note that the second sentence of σ(e) implies that shared bidders wait for all dedicated bidders to enter and finish their bidding before bidding in a situation in which both auctions have the same standing bid. This implication is used directly within the proofs of Claims 3 and Lemma 2 (subcase (b2) in the latter).