Interconnected Pay-As-Bid Auctions

I develop a framework to study common situations, in which substitute goods are sold in separate, good-specific multi-unit (pay-as-bid) auctions. I characterize bidding behavior and investigate auction design features that could increase revenues. The setting I develop gives rise to an essentially unique symmetric Nash equilibrium in which bidders shade their bids more strongly when goods are close substitutes. To increase revenues, the seller can offer total supply quantities that are (stochastically) unequal in size. This fosters more aggressive bidding and provides a rationale to hold separate, parallel auctions instead of selling all in one auction.