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Register a new userA heuristic for estimating Nash equilibria in first-price auctions with correlated values
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Added by
Benjamin Heymann
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Our paper concerns the computation of Nash equilibria of first-price auctions with correlated values. While there exist several equilibrium computation methods for auctions with independent values, the correlation of the bidders values introduces significant complications that render existing methods unsatisfactory in practice. Our contribution is a step towards filling this gap: inspired by the seminal fictitious play process of Brown and Robinson, we present a learning heuristic-that we call fictitious bidding (FB)-for estimating Bayes-Nash equilibria of first-price auctions with correlated values, and we assess the performance of this heuristic on several relevant examples.
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We study correlated equilibria and coarse equilibria of simple first-price single-item auctions in the simplest auction model of full information. Nash equilibria are known to always yield full efficiency and a revenue that is at least the second-highest value. We prove that the same is true for all correlated equilibria, even those in which agents overbid -- i.e., bid above their values. Coarse equilibria, in contrast, may yield lower efficiency and revenue. We show that the revenue can be as low as 26% of the second-highest value in a coarse equilibrium, even if agents are assumed not to overbid, and this is tight. We also show that when players do not overbid, the worst-case bound on social welfare at coarse equilibrium improves from 63% of the highest value to 81%, and this bound is tight as well.
This paper studies equilibrium quality of semi-separable position auctions (known as the Ad Types setting) with greedy or optimal allocation combined with generalized second-price (GSP) or Vickrey-Clarke-Groves (VCG) pricing. We make three contributions: first, we give upper and lower bounds on the Price of Anarchy (PoA) for auctions which use greedy allocation with GSP pricing, greedy allocations with VCG pricing, and optimal allocation with GSP pricing. Second, we give Bayes-Nash equilibrium characterizations for two-player, two-slot instances (for all auction formats) and show that there exists both a revenue hierarchy and revenue equivalence across some formats. Finally, we use no-regret learning algorithms and bidding data from a large online advertising platform and no-regret learning algorithms to evaluate the performance of the mechanisms under semi-realistic conditions. For welfare, we find that the optimal-to-realized welfare ratio (an empirical PoA analogue) is broadly better than our upper bounds on PoA; For revenue, we find that the hierarchy in practice may sometimes agree with simple theory, but generally appears sensitive to the underlying distribution of bidder valuations.
First price auctions are widely used in government contracts and industrial auctions. In this paper, we consider the Bayesian Nash Equilibrium (BNE) in first price auctions with discrete value distributions. We study the characterization of the BNE in the first price auction and provide an algorithm to compute the BNE at the same time. Moreover, we prove the existence and the uniqueness of the BNE. Some of the previous results in the case of continuous value distributions do not apply to the case of discrete value distributions. In the meanwhile, the uniqueness result in discrete case cannot be implied by the uniqueness property in the continuous case. Unlike in the continuous case, we do not need to solve ordinary differential equations and thus do not suffer from the solution errors therein. Compared to the method of using continuous distributions to approximate discrete ones, our experiments show that our algorithm is both faster and more accurate. The results in this paper are derived in the asymmetric independent private values model, which assumes that the buyers value distributions are common knowledge.
Since 2019, most ad exchanges and sell-side platforms (SSPs), in the online advertising industry, shifted from second to first price auctions. Due to the fundamental difference between these auctions, demand-side platforms (DSPs) have had to update their bidding strategies to avoid bidding unnecessarily high and hence overpaying. Bid shading was proposed to adjust the bid price intended for second-price auctions, in order to balance cost and winning probability in a first-price auction setup. In this study, we introduce a novel deep distribution network for optimal bidding in both open (non-censored) and closed (censored) online first-price auctions. Offline and online A/B testing results show that our algorithm outperforms previous state-of-art algorithms in terms of both surplus and effective cost per action (eCPX) metrics. Furthermore, the algorithm is optimized in run-time and has been deployed into VerizonMedia DSP as production algorithm, serving hundreds of billions of bid requests per day. Online A/B test shows that advertisers ROI are improved by +2.4%, +2.4%, and +8.6% for impression based (CPM), click based (CPC), and conversion based (CPA) campaigns respectively.
We study the problem of selling a good to a group of bidders with interdependent values in a prior-free setting. Each bidder has a signal that can take one of $k$ different values, and her value for the good is a weakly increasing function of all the bidders signals. The bidders are partitioned into $ell$ expertise-groups, based on how their signal can impact the values for the good, and we prove upper and lower bounds regarding the approximability of social welfare and revenue for a variety of settings, parameterized by $k$ and $ell$. Our lower bounds apply to all ex-post incentive compatible mechanisms and our upper bounds are all within a small constant of the lower bounds. Our main results take the appealing form of ascending clock auctions and provide strong incentives by admitting the desired outcomes as obvious ex-post equilibria.
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