Generalized Second Price Auction Research Articles

A Cost-Aware Utility-Maximizing Bidding Strategy for Auction-Based Federated Learning.

Auction-based federated learning (AFL) has emerged as an efficient and fair approach to incentivize data owners (DOs) to contribute to federated model training, garnering extensive interest. However, the important problem of helping data consumers (DCs) bid for DOs in competitive AFL settings remains open. Existing work simply treats that the actual cost paid by a winning DC (i.e., the bid cost) is equal to the bid price offered by that DC itself. However, this assumption is inconsistent with the widely adopted generalized second-price (GSP) auction mechanism used in AFL, including in these existing works. Under a GSP auction, the winning DC does not pay its own proposed bid price. Instead, the bid cost for the winner is determined by the second-highest bid price among all participating DCs. To address this limitation, we propose a first-of-its-kind federated cost-aware bidding strategy () to help DCs maximize their utility under GSP auction-based federated learning (FL). It enables DCs to efficiently bid for DOs in competitive AFL markets, maximizing their utility and improving the resulting FL model accuracy. We first formulate the optimal bidding function under the GSP auction setting, and then demonstrate that it depends on utility estimation and market price modeling, which are interrelated. Based on this analysis, jointly optimizes in a novel end-to-end framework, and then executes the proposed return on investment (ROI)-based method to determine the optimal bid price for each piece of the data resource. Through extensive experiments on six commonly adopted benchmark datasets, we show that outperforms eight state-of-the-art methods, beating the best baseline by 4.39%, 4.56%, 1.33%, and 5.43% on average in terms of the total amount of data obtained, number of data samples per unit cost, total utility, and FL model accuracy, respectively.

Learning and pricing models for repeated generalized second-price auction in search advertising

In search advertising how much an advertiser is willing to pay for a click or tap on his search ad is private information, which hampers an ad seller’s ability to set the best reserve price to increase the revenue for the generalized second-price (GSP) auctions used to allocate ad slots. We present a series of learning and pricing models for repeated GSP auctions selling multiple heterogeneous items. This paper contributes to the literature in dynamic pricing with learning and complements the existing off-line studies on impact of the reserve price in the multi-billion dollar online advertising business. With few restrictions on the distribution function of the unknown parameter, algorithms are developed to estimate the empirical distribution function and determine the best reserve price to reduce the revenue loss (regret) over time. When bidders bid in the locally envy-free equilibrium, we present an algorithm that has the best attainable regret upper bound. When bidders do not bid in the locally envy-free equilibrium, we propose a GSP auction with position-specific reserve prices and develop an algorithm with the same regret bound to mitigate the risk of strategic bidding. With a high volatility involved, learning becomes more active while earning is more effective. When bidders coordinate bidding, the properly selected starting reserve prices can substantially reduce the revenue loss from possible collusive bidding behaviors.

A novel GSP auction mechanism for ranking Bitcoin transactions in blockchain mining

Bitcoin is gaining ground in recent years. In the Bitcoin system, miners provide computing power to confirm transactions and mine blocks in pursuit of transaction fees, while users compete by bidding transaction fees for faster confirmation. This process is in essence analogous to online ad auctions, where advertisers bid for more prominent ad slots. Therefore, inspired by the Generalized Second Price (GSP) mechanism dominantly used in online ad auctions, we propose to adopt the GSP auction model in the Bitcoin transaction confirmation game. Also, we use weighted fees as the new ranking basis, which can be calculated by user-submitted fees, transaction size, quality scores and virtual fees accumulated from the waiting time. We show that the formulated static GSP transaction fee auction with complete information has a unique Pure Strategy Nash Equilibrium. Then, we discuss the impacts of quality scores and virtual fees on users' equilibrium fee decisions and payoffs. Finally, computational experiments are designed to validate our theoretical models and analysis. Our research findings indicate that this novel GSP mechanism is superior to the currently adopted GFP mechanism, and can help users save fees. Besides, quality scores and virtual fees are also proven to be effective on reducing users' paid fees. Moreover, the design of virtual fees allows all transactions to be processed more efficiently in a uniform pipeline, and the interests of transactions with and without associated fees are taken into consideration.

Generalized Second Price Auctions over a Network

We consider the problem of how to apply a generalized second price (GSP) auction to a buyer–seller network. GSP auctions are often used to sell online ads where buyers care about the position or placement of the ad. GSP auctions can also be applied to wireless data transmissions with congestion where buyers care about the speed of data transmission; however, such an auction would take place over a network as a buyer could only purchase from a seller (or cell tower) that he was linked to (or was close to). Two GSP auctions over a network are considered: separate GSP auctions, and integrated GSP auctions with pauses. The efficiency of these auctions is examined with efficiency favoring the integrated auction with pauses.

Matching Value and Market Design in Online Advertising Networks: An Empirical Analysis

Advertising networks have recently played an increasingly important role in the online advertising market. Critical to the success of an advertising network are two mechanisms: an allocation mechanism that efficiently matches advertisers with publishers and a pricing scheme that maximally extracts surplus from the matches. In this paper, we quantify the value and investigate the determinants of a successful advertiser-publisher match, using data from Taobao’s advertising network. A counterfactual experiment reveals that the platform’s profit under a decentralized allocation mechanism is close to the profit level when the platform centrally assigns the matching under perfect platform knowledge of matching values. In another counterfactual experiment, we explore the effect of platform technology and revenue model on the strategic choice of the pricing schemes of list price versus generalized second price (GSP) auction pricing. We find that platforms that profit from the advertiser side may have less incentive to adopt GSP auction than platforms that profit from the publisher side.

On the Stability of Generalized Second Price Auctions with Budgets

The Generalized Second Price (GSP) auction used typically to model sponsored search auctions does not include the notion of budget constraints, which is present in practice. Motivated by this, we introduce the different variants of GSP auctions that take budgets into account in natural ways. We examine their stability by focusing on the existence of Nash equilibria and envy-free assignments. We highlight the differences between these mechanisms and find that only some of them exhibit both notions of stability. This shows the importance of carefully picking the right mechanism to ensure stable outcomes in the presence of budgets.

Keyword Search Advertising and First-Page Bid Estimates: A Strategic Analysis

In using the generalized second-price (GSP) auction to sell advertising slots, a search engine faces several challenges. Advertisers do not truthfully bid their valuations, and the valuations are uncertain. Furthermore, advertisers are budget constrained. In this paper we analyze a stylized model of the first-page bid estimate (FPBE) mechanism first developed by Google and demonstrate its advantages in dealing with these challenges. We show why and when the FPBE mechanism yields higher profits for the search engine compared with the traditional GSP auction and the GSP auction with advertiser-specific minimum bid. In the event that a high-valuation advertiser is budget constrained, the search engine can use the FPBE mechanism to alter the listing order with the intent of keeping the high-valuation advertiser in the auction for a longer time. The resulting increase in the search engine’s profits is not necessarily at the expense of the advertisers because the combined profits of the advertisers and the search engine increase. This paper was accepted by J. Miguel Villas-Boas, marketing.

Revenue Guarantees in the Generalized Second Price Auction

Sponsored search auctions are the main source of revenue for search engines. In such an auction, a set of utility maximizing advertisers competes for a set of ad slots. The assignment of advertisers to slots depends on the bids they submit; these bids may be different than the true valuations of the advertisers for the slots. Variants of the celebrated VCG auction mechanism guarantee that advertisers act truthfully and, under some assumptions, lead to revenue or social welfare maximization. Still, the sponsored search industry mostly uses generalized second price (GSP) auctions; these auctions are known to be nontruthful and suboptimal in terms of social welfare and revenue. In an attempt to explain this tradition, we study a Bayesian setting wherein the valuations of advertisers are drawn independently from a common regular probability distribution. In this setting, it is well known from the work of Myerson [1981] that the optimal revenue is obtained by the VCG mechanism with a particular reserve price that depends on the probability distribution. We show that, by appropriately setting the reserve price, the revenue over any Bayes-Nash equilibrium of the game induced by the GSP auction is at most a small constant factor away from the optimal revenue, improving previous results of Lucier et al. [2012]. Our analysis is based on the Bayes-Nash equilibrium conditions and the improved results are obtained by bounding the utility of each player at equilibrium using infinitely many deviating bids and also by developing novel prophet-like inequalities.

Optimal Bidding Strategies and Equilibria in Dynamic Auctions with Budget Constraints

How should agents bid in repeated sequential auctions when they are budget constrained? A motivating example is that of sponsored search auctions, where advertisers bid in a sequence of generalized second price (GSP) auctions. These auctions, specifically in the context of sponsored search, have many idiosyncratic features that distinguish them from other models of sequential auctions: First, each bidder competes in a large number of auctions, where each auction is worth very little. Second, the total bidder population is often large, which means it is unrealistic to assume that the bidders could possibly optimize their strategy by modeling specific opponents. Third, the presence of a virtually unlimited supply of these auctions means bidders are necessarily expense constrained. Motivated by these three factors, we first frame the generic problem as a discounted Markov Decision Process for which the environment is independent and identically distributed over time. We also allow the agents to receive income to augment their budget at a constant rate. We first provide a structural characterization of the associated value function and the optimal bidding strategy, which specifies the extent to which agents underbid from their true valuation due to long term budget constraints. We then provide an explicit characterization of the optimal bid shading factor in the limiting regime where the discount rate tends to zero, by identifying the limit of the value function in terms of the solution to a differential equation that can be solved efficiently. Finally, we proved the existence of Mean Field Equilibria for both the repeated second price and GSP auctions with a large number of bidders.

Pure-Strategy Nash Equilibria of GSP Keyword Auction

Despite the tremendous commercial success of generalized second-price (GSP) keyword auctions, it still remains a big challenge for an advertiser to formulate an effective bidding strategy. In this paper, we strive to bridge this gap by proposing a framework for studying pure-strategy Nash equilibria in GSP auctions. We first analyze the equilibrium bidding behaviors by investigating the properties and distribution of all pure-strategy Nash equilibria. Our analysis shows that the set of all pure-strategy Nash equilibria of a GSP auction can be partitioned into separate convex polyhedra based on the order of bids if the valuations of all advertisers are distinct. We further show that only the polyhedron that allocates slots efficiently is weakly stable, thus allowing all inefficient equilibria to be weeded out. We then propose a novel refinement method for identifying a set of equilibria named the stable Nash equilibrium set (STNE) and prove that STNE is either the same as or a proper subset of the set of the well-known symmetrical Nash equilibria. These findings free both auctioneers and advertisers from complicated strategic thinking. The revenue of a GSP auction on STNE is at least the same as that of the classical Vickrey-Clarke-Groves mechanism and can be used as a benchmark for evaluating other mechanisms. At the same time, STNE provides advertisers a simple yet effective and stable bidding strategy.

On Expressing Value Externalities in Position Auctions

We introduce a bidding language for expressing negative value externalities in position auctions for online advertising. The unit-bidder constraints (UBC) language allows a bidder to condition a bid on its allocated slot and on the slots allocated to other bidders. We introduce a natural extension of the Generalized Second Price (GSP) auction, the expressive GSP (eGSP) auction, that induces truthful revelation of constraints for a rich subclass of unit-bidder types, namely downward-monotonic UBC. We establish the existence of envy-free Nash equilibrium in eGSP under a further restriction to a subclass of exclusion constraints, for which the standard GSP has no pure strategy Nash equilibrium. The equilibrium results are obtained by reduction to equilibrium analysis for reserve price GSP (Even-Dar et al. 2008). In considering the winner determination problem, which is NP-hard, we bound the approximation ratio for social welfare in eGSP and provide parameterized complexity results.

Equilibrium Bidding Strategy for GSP Keyword Auctions

The generalized second-price (GSP) mechanism is the most widely-used auction format in sponsored search markets. However, figuring out how to bid on GSP auctions presents major theoretical and computational challenges due to the complex nature of the auction format and the infinite number of equilibria. Our study characterizes various equilibrium bidding behaviors in GSP auctions. We develop an algorithm to identify all pure-strategy Nash equilibria and discuss their distribution in the pure-strategy space. This equilibrium distribution can help advertisers formulate bidding strategies, and help search engines calculate their expected revenues.

Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords

Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords

Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords

We investigate the “generalized second-price” (GSP) auction, a new mechanism used by search engines to sell online advertising. Although GSP looks similar to the Vickrey-Clarke-Groves (VCG) mechanism, its properties are very different. Unlike the VCG mechanism, GSP generally does not have an equilibrium in dominant strategies, and truth-telling is not an equilibrium of GSP. To analyze the properties of GSP, we describe the generalized English auction that corresponds to GSP and show that it has a unique equilibrium. This is an ex post equilibrium, with the same payoffs to all players as the dominant strategy equilibrium of VCG. (JEL D44, L81, M37)