2015/04/30 by Zheng Wen, Wen, Zheng, Eric Bax +3
Business, Management and Accounting · Decision Sciences · Social Sciences · #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #Consumer Market Behavior and Pricing #Experimental Behavioral Economics Studies #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.1504.08333
openalex publication_date 2015/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In quasi-proportional auctions, each bidder receives a fraction of the allocation equal to the weight of their bid divided by the sum of weights of all bids, where each bid's weight is determined by a weight function. We study the relationship between the weight function, bidders' private values, number of bidders, and the seller's revenue in equilibrium. It has been shown that if one bidder has a much higher private value than the others, then a nearly flat weight function maximizes revenue. Essentially, threatening the bidder who has the highest valuation with having to share the allocation maximizes the revenue. We show that as bidder private values approach parity, steeper weight functions maximize revenue by making the quasi-proportional auction more like a winner-take-all auction. We also show that steeper weight functions maximize revenue as the number of bidders increases. For flatter weight functions, there is known to be a unique pure-strategy Nash equilibrium. We show that a pure-strategy Nash equilibrium also exists for steeper weight functions, and we give lower bounds for bids at an equilibrium. For a special case that includes the two-bidder auction, we show that the pure-strategy Nash equilibrium is unique, and we show how to compute the revenue at equilibrium. We also show that selecting a weight function based on private value ratios and number of bidders is necessary for a quasi-proportional auction to produce more revenue than a second-price auction.