Title: Proportional Allocation Share Auctions
We analyze a mobile web advertising auction employing a proportional allocation rule where advertisements are shown with frequency in proportion to bids. Real-world auctions currently use a second-price rule, but we show that such an auction admits no pure-strategy Nash equilibria. Instead, we propose the use of a first-price rule (FPP), and show the existence of a unique pure-strategy Nash equilibrium in a one-shot complete information game. In a dynamic game of incomplete information, we demonstrate in simulation that bids converge to this Nash equilibrium quickly. We also show that by tuning a single parameter in the FPP allocation rule, the auctioneer can make trade-offs between revenue and efficiency. We compare FPP with the maximally-efficient Vickrey-Clarke-Groves (VCG) auction, and find in simulation that FPP efficiency is at least 80% as efficient as VCG.