Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revenue-Maximizing Mechanism Design for Quasi-Proportional Auctions   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.

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The categories of this paper are: q-fin
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph