Equitable Pricing in Auctions
arxiv(2024)
摘要
We study how pricing affects the division of surplus among buyers in auctions
for multiple units. Our equity objective may be important, e.g., for
competition concerns in downstream markets, complementing the long-standing
debate on revenue and efficiency. We study a canonical model of auctions for
multiple indivisible units with unit demand buyers and valuations with a
private and a common component and consider all pricing rules that are a
mixture (i.e., a convex combination) of pay-as-bid and uniform pricing. We
propose the winners' empirical variance (WEV), the expected empirical variance
of surplus among the winners, as a metric for surplus equity. We show that, for
a range of private-common value proportions, a strictly interior mix of
pay-as-bid and uniform pricing minimizes WEV. From an equity perspective,
auctions with a higher private value component benefit from more price
discrimination, whereas only auctions with a sufficiently high common value
justify a more uniform pricing rule. We provide a criterion under which
strictly mixed pricing dominates uniform pricing, a partial ranking of
different mixed pricing formats, and bounds on the WEV-minimizing pricing under
the assumption of log-concave signal distributions. In numerical experiments,
we further illustrate the WEV-minimal pricing as a function of the
private-common-value mix.
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