Second-price Auction Research Articles

Beyond the VCG mechanism: truthful reverse auctions for relay selection with high data rates, high base station utility and low interference in D2D networks

Device-to-Device communication allows a cellular user (relay node) to relay data between the base station (BS) and another cellular user (destination node). We address the problem of designing reverse auctions to assign a relay node to each destination node, when there are multiple potential relay nodes and multiple destination nodes, in the scenarios where the transmission powers of the relay nodes are: 1) fixed, 2) selected to achieve the data rates desired by destination nodes, and 3) selected so as to approximately maximize the BS's utility. We show that auctions based on the widely used Vickrey-Clarke-Groves (VCG) mechanism have several limitations in scenarios 1) and 2); also, in scenario 3), the VCG mechanism is not applicable. Hence, we propose novel reverse auctions for relay selection in each of the above three scenarios. We prove that all the proposed reverse auctions can be truthfully implemented as well as satisfy the individual rationality property. Using numerical computations, we show that in scenarios 1) and 2), our proposed auctions significantly outperform the auctions based on the VCG mechanism in terms of the data rates achieved by destination nodes, utility of the BS and/ or the interference cost incurred to the BS.

Premium auctions in the field

In a field experiment, we study the revenue-generating properties of premium auctions. In a premium auction, the runner-up obtains a premium for driving up the price paid by the winner. Previous research, both theoretical and in the lab, has shown that the relative performance of premium auctions compared to standard auction formats is context-specific. In the experiment, we compare two types of premium auctions with the standard Vickrey auction selling high-quality, limited-edition posters in an online auction. We observe that neither premium auction raises higher revenue than the Vickrey auction. Revenue dispersion in the Amsterdam auction, one of the premium auctions, is lower than that in the other two auctions.

Pricing Carpool Rides Based on Schedule Displacement

This paper considers a carpool matching (CaMa) problem in which participants price shared rides based on both operating cost and schedule displacement (i.e., the absolute difference between the desired and actual arrival times). By reporting their valuation of this displacement, each participant in effect bids for every possible shared ride that generates a unique value to her. The CaMa problem can be formulated as a mixed integer program (MIP) that maximizes the social welfare by choosing matching pairs and a departure time for each pair. We show the optimal departure time can be determined for each pair a priori, independent of the matching problem. This result reduces the CaMa problem to a standard bipartite matching problem. We prove that the classical Vickrey-Clarke-Groves (VCG) pricing policy ensures no participant is worse off or has the incentive to misreport their valuation of schedule displacement. To control the large deficit created by the VCG policy, we develop a single-side reward (SSR) pricing policy, which only compensates participants who are forced by the system to endure a schedule displacement. Under the assumption of overpricing tendency (i.e., no participant would want to underreport their value), we show the SSR policy not only generates substantial profits, but also retains the other desired properties of the VCG policy, notably truthful reporting. Even though it cannot rule out underreporting, our simulation experiments confirm that the SSR policy is a robust and deficit-free alternative to the VCG policy. Specifically, we find that (1) underreporting is not a practical concern for a carpool platform as it never reduces the number of matched pairs and its impact on profits is largely negligible; and (2) participants have very little to gain by underreporting their value.

Shill bidding and trust

Shill bidding occurs when the seller enters a bid for her own item. A bidder forms expectations about whether the seller is participating and must decide whether to trust that she is not engaging in what may be viewed as an unkind practice. A trusting individual can be expected to respond differently than an untrusting one. Auctions with the potential for shill bidding allow for trust to be expressed. We design an experiment considering first and second-price auctions with and without the potential for shill bidding. A Trust Game is used to measure trust. We document that the potential for shill bidding leads to lower bids being submitted. Heterogeneous effects are explored. Bidding behavior can be explained in part by one’s level of trust and expectations of other’s trust. In first-price auctions, less trusting individuals submit lower bids and respond to the potential for shill bidding by lowering their bids. In second-price auctions, subjects with lower expectations of the trust others have bid less and respond to shill bidding by further lowering their bid. Second, sellers engage in shill bidding but rarely win. Third, the potential for shill bidding adversely affects revenue and allocative efficiency.

The Referrer's Dilemma

If buyers can only participate via referrals, referral monotonicity holds in the Vickrey-Clarke-Groves (VCG) mechanism, i.e., any buyer's payoff weakly increases as her connection (i.e., referable buyers) expands. However, if every buyer expands her connection, buyers are weakly worse off and the seller is weakly better off, which we call the referrer's dilemma. The referrer's dilemma occurs in any mechanism that is referral monotone, individually rational, threshold-pricing, and rewarding for individual contribution. We also show that in the VCG mechanism, the winner is better off and the seller is worse off under the referrer's dilemma with shill bidding.

Pricing Carpool Rides Based on Schedule Displacement

This paper considers a carpool matching (CaMa) problem in which participants price shared rides based on both operating cost and schedule displacement (i.e, the absolute difference between the desired and actual arrival times). By reporting their valuation of this displacement, each participant in effect bids for every possible shared ride that generates a unique value to her. The CaMa problem can be formulated as a mixed integer program (MIP) that maximizes the social welfare by choosing matching pairs and a departure time for each pair. We show the optimal departure time can be determined for each pair a priori, independent of the matching problem. This result reduces the CaMa problem to a standard bipartite matching problem. We prove that the classical Vickrey-Clarke-Groves (VCG) pricing policy ensures no participant is worse off or has the incentive to misreport their valuation of schedule displacement. To control the large deficit created by the VCG policy, we develop a single-side reward (SSR) pricing policy, which only compensates participants who are forced by the system to endure a schedule displacement. Under the assumption of overpricing tendency (i.e., no participant would want to underreport their value), we show the SSR policy not only generates substantial profits, but also retains the other desired properties of the VCG policy, notably truthful reporting. Even though it cannot rule out underreporting, our simulation experiments confirm that the SSR policy is a robust and deficit-free alternative to the VCG policy. Specifically, we find that (1) underreporting is not a practical concern for a carpool platform as it never reduces the number of matched pairs and its impact on profits is largely negligible; and (2) participants have very little to gain by underreporting their value.

Tight revenue gaps among simple and optimal mechanisms

Consider a fundamental problem in microeconomics: selling a single item to a number of potential buyers, who independently draw their values from regular and publicly known distributions. There are four mechanisms widely studied in the literature and widely used in practice: Myerson Auction (OPT), Sequential Posted Pricing (SPM), Second-Price Auction with Anonymous Reserve (AR) , and Anonymous Pricing (AP). OPT is revenue-optimal but complicated, which also experiences several practical issues such as fairness. AP is the simplest mechanism, but also generates the lowest revenue among these four mechanisms. SPM and AR are of intermediate complexity and revenue. A quantitative approach to comparing the relative power of these mechanisms is to study their revenue gaps, each of which is defined as the largest ratio between the revenues from a pair of mechanisms. This letter surveys some recent developments on establishing tight revenue gaps, and highlights some open questions.

The Crowdfunding Effects on Venture Capital Investments

We study how crowdfunding, as a source of public information, affects competing venture capital (VC) firms' investment decisions in terms of the timing, likelihood, and expected amount of VC investment in a startup. Our economy consists of one startup, one crowdfunding platform, and two VC firms with differing prior beliefs about the startup's probability of success. The startup first approaches both VC firms for funding, which is modeled as a second-price auction between the two firms, and then turns to the crowdfunding platform if rejected by both. After the crowdfunding, the VC firms update their assessments of the startup's success based on the information collected from the crowdfunding platform, and the startup seeks funding from them again. We find that crowdfunding and the competition between the VC firms raise the expected amount of VC investment. Moreover, crowdfunding increases the chance of a startup receiving VC funding only for those startups deemed unfavorable by both VC firms; for debatable startups about which VC firms' views diverge, crowdfunding may reduce their chance of receiving VC investment. We then examine how the relationship between crowdfunding and VC investment is shaped by the characteristics of the startup and the crowdfunding platform. For instance, when the more optimistic VC firm has a moderate expectation for the startup and the investment risk is high (resp., low), that VC firm tends to invest before the startup seeks crowdfunding if the crowdfunding information is sufficiently accurate (resp., noisy). Finally, we observe more nuanced crowdfunding effects in several model extensions, for example, if the startup is allowed to strategically decide on the timing to receive a VC investment, and if VC firms can observe private signals on the startup.

Incentive Mechanism for Clearing Energy and Reserve Markets in Multi-Area Power Systems

The increasing integration of renewable energy has highlighted the importance of interchange trading in multi-area power systems (MAPS). In some existing multi-area electricity markets, the marginal-pricing (MP) mechanism is adopted. However, this mechanism is known to lose market efficiency when profit-maximizing units strategically bid to manipulate electricity prices. To elicit truthful bids from generators and guarantee the optimality of MAPS, we propose an incentive mechanism based on Vickrey-Clarke-Groves (VCG) auction. A two-stage multi-area economic dispatch model for joint energy and reserve clearing is formulated with hybrid AC/DC links. We illustrate that when settled by the MP mechanism, thermal units have incentive to strategically bid on reserve prices, thereby preventing inter-area power exchange. The VCG-based mechanism sets up the payment to a unit as other generators’ incremental costs after removing it in the market clearing process, which reveals the externality induced by this unit and thus incentivizes truthful bids. To preserve each area's autonomy, a novel decentralized algorithm based on improved optimality condition decomposition is developed. Case studies based on a 2-area 60-bus system and a 3-area 354-bus system demonstrate the effectiveness and efficiency of the proposed mechanism and method.

Mitigating Risk Selection in Health Care Entitlement Programs: A Patient-Level Competitive Bidding Approach

Health care entitlement programs in the U.S. represent a large and growing financial outlay for taxpayers. In the pursuit of operational efficiencies, program administrators often contract with private managed care organizations (MCOs) to procure insurance for beneficiaries. This, however, encourages MCOs to attract the healthiest beneficiaries and avoid the sickest; a phenomenon known as risk selection. This leaves the sickest patients to potentially seek care in safety net facilities or emergency rooms. A mechanism that improves beneficiaries’ access to care without increasing costs would be invaluable to managers and policymakers. This paper investigates whether risk selection can be mitigated with a mechanism where MCOs bid to enroll individual beneficiaries. Although procurement auctions have been studied extensively in the literature, extant research has rarely discussed individual-level bidding. Using game theory, we model an entitlement program under three payment mechanisms: risk-adjustment, bidding, and a mix of prospective payment and bidding. Analytical results show that traditional risk-adjustment cannot optimally be used to eliminate risk selection, while either bidding mechanism eliminates it entirely. Mixed bidding eliminates risk selection at a strictly lower cost than pure bidding. The proposed mixed bidding approach is a new type of mechanism with pre-auction offers that strictly dominates the second-price auction without requiring additional assumptions. Numerical analysis shows bidding dominates risk adjustment in 73.1 percent of simulated parameter sets. Compared to risk adjustment, bidding enrolls 12.1 percent more beneficiaries at 12.7 percent lower cost. Sensitivity analysis reveals that the proposed bidding mechanism dominates in scenarios that more closely resemble real-world health care entitlement environments. More remarkably, bidding would likely generate more cost savings in jurisdictions with a large population of higher risk beneficiaries. These results show that individual-level auctions are a promising mechanism for achieving the dual aim of financial sustainability and expanded access to care for the most vulnerable.

Overbidding and matching rules in second-price auctions: An experimental study

This paper examines how matching conditions – stranger, partner, and group – in the second-price auction (SPA) affect the extent to which spite contributes to overbidding. In my theoretical framework, bidders experience negative spillovers from rivals’ payoffs and also a joy-of-winning (JOW). I derive maximum likelihood estimates of the spite and JOW parameters using 80% of the data, and find that the weights assigned to rivals’ payoffs in subjects’ utility functions are 8% and 15% in partner and group treatments respectively. Next, I evaluate the fits of the pure spite, pure JOW, and the combined models in the estimation and prediction sample, i.e., in the remaining 20% of subjects. Consistent with the estimation results, the goodness-of-fit statistics suggest that spite is more important in driving overbidding when bidders are matched against each other repeatedly. Further, I show that overbidding increases more in the partner treatment relative to the stranger treatment in the middle rounds of auctions. Finally, by eliciting subjects’ willingness-to-pay to harm others, I am able to link negative other-regarding preferences to overbidding and estimates of spitefulness in the SPA. This affirms the hypothesis that social motivation influences bidding behaviour in auctions with repeated interactions.

The Net Effect of Advice on Strategy-Proof Mechanisms: An Experiment for the Vickrey Auction

We conduct laboratory experiments for the multi-unit Vickrey auction with and without advice to subjects on strategy-proofness. The rate of truth-telling among the subjects without advice stays at 20%, whereas the rate increases to 47% among those who have received advice. By conducting similar experiments for the pay-your-bid auction, which is not strategy-proof, we confirm that the increase in truth-telling is due significantly to the net advice effect (i.e., the effect beyond the so-called experimenter demand effect). Moreover, we find that providing advice improves efficiency in the Vickrey auction, particularly in the early periods, when the subjects are less experienced. In general, subjects tend to overbid in Vickrey auction experiments. Our results indicate the possibility that providing simple advice decreases such overbidding by promoting a better understanding of the strategy-proofness of the Vickrey auction. Strategy-proof mechanisms are sometimes criticized because players often fail to recognize the benefit of telling the truth. However, our observations show that introducing advice on the property of strategy-proofness helps them behave “correctly.”

Credibility in Second-Price Auctions: An Experimental Test

We provide the first direct test of how the credibility of an auction format affects bidding behavior and final outcomes. To do so, we conduct a series of laboratory experiments where the role of the seller is played by a human subject who receives the revenue from the auction and who (depending on the treatment) has agency to determine the outcome of the auction. We find that a large majority of bids in the non-credible version of the second-price auction lie between the theoretical benchmarks of the first-price auction and the credible second-price auction. While sellers in the non-credible second-price auction often break the rules of the auction and overcharge the winning bidder, they typically do not maximize revenue. We provide a behavioral explanation for our results based on incorrect beliefs (on the part of bidders) and aversion to rule-breaking (on the part of sellers), which is confirmed by revealed preference tests.

Efficient multiunit auctions for normal goods

I study multiunit auction design when bidders have private values, multiunit demands, and non‐quasilinear preferences. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. I give conditions under which we can design a mechanism that retains the Vickrey auction's desirable incentive and efficiency properties: (1) individual rationality, (2) dominant strategy incentive compatibility, and (3) Pareto efficiency. I show that there is a mechanism that retains the desired properties of the Vickrey auction if there are two bidders who have single‐dimensional types. I also present an impossibility theorem that shows that there is no mechanism that satisfies Vickrey's desired properties and weak budget balance when bidders have multidimensional types.

The Groupwise-Pivotal Referral Mechanism: Core-Selecting Referral Strategy-Proof Mechanism

We introduce the groupwise-pivotal referral (GPR) mechanism for auctions where buyers can participate only through referrals. Each buyer's type consists of a valuation and referable buyers. Unlike the second-price auction (SPA), the Vickrey-Clarke-Groves (VCG) mechanism provides referral incentives. However, VCG is not budget-feasible. In contrast, GPR is core-selecting, implying efficiency and budget feasibility. In GPR, bidders should refer truthfully and have no incentive to underbid. GPR is shill-proof and groupwise collusion-proof. Furthermore, GPR's ex-post revenue outperforms both VCG and SPA. We also study more general environments than auctions.

ABCrowd An Auction Mechanism on Blockchain for Spatial Crowdsourcing

In this paper, a fully distributed auction-blockchain-based crowdsourcing framework is proposed- ABCrowd . In a typical crowdsourcing framework, independent workers compete to be allocated requesters’ tasks. These workers advertise their costs to the centralized platform, which then decides the final allocation of tasks. While performing the allocation, centralized platforms face two main challenges: 1) how to ensure trusted execution for the allocation of tasks, and 2) how to motivate workers to declare their truthful costs. To address these challenges, ABCrowd proposes to run the crowdsourcing platform entirely on Ethereum Blockchain while incorporating auctions. Blockchain and smart contracts guarantee trusted execution for the allocation through autonomous and transparent on-Chain execution. ABCrowd uses the Repeated-Single-Minded Bidder (R-SMB) auction mechanism, which motivates workers to bid truthfully before allocating them and calculating their payments. R-SMB is an approximation of the optimized off-Chain Vickrey-Clarke-Groves (VCG) mechanism in terms of maximized profit. It entails repeating the Single-Minded Bidder (SMB) auction mechanism to meet the allocation requirement of crowdsourcing applications. ABCrowd is implemented and evaluated using Solidity on a private Ethereum Blockchain, where a real publicly available dataset is used. The proposed on-Chain R-SMB auction mechanism is compared to the off-Chain VCG mechanism, where the results show that R-SMB provides similar performance to VCG in terms of the average number of allocated tasks. Furthermore, R-SMB outperforms VCG in workers’ travelled distance and requesters’ costs, at a low execution cost.

A VCG Mechanism for Demand Management of Irrigation Systems

Global climate change has induced changes in snow covers and precipitation patterns leading to unreliable availability of surface water for agricultural usage. Moreover, the increasing population has put additional strains on precious freshwater resources such as groundwater, leading to unsustainable practices of agriculture. Many studies suggest that demand based surface water management instead of supply based management may greatly mitigate the problem of supply-side fluctuations. Moreover, the rigidity of supply-based distribution rosters and fixed tariffs may be overcome using flexible pricing schemes. In this work, we propose a demand-driven allocation scheme for irrigation canal water enabled by the use of precision sensor technologies. The allocation is coupled with an auction based pricing mechanism. In the proposed approach, the demand can be met using surface water from an irrigation canal network, which is regulated by a principal agent such as a regulatory authority. In the face of shortage, the farmers resort to expensive pumping of non-renewable groundwater to meet their demand. A cropping season is divided into equal slots of fixed duration. At the beginning of each time slot, the principal-agent solicits the valuations of the farmers and sorts the bids received from the players in decreasing order and starts fulfilling the demands from the top. The principal agent uses Vickrey Clarke Groves (VCG) mechanism to compute the payments. The VCG mechanism for payments ensures user truthfulness. Our simulation results demonstrate that under certain realistic assumptions, this mechanism can increase profitability by reducing costs, help decrease groundwater pumping and conserve the surface water.

Truth-Telling Dominating Strategy: Impossibilities of Shill-Proofness

A strategy is truth-telling dominating (TTD) if it weakly (strictly, resp.) dominates truth-telling for all (some, resp.) strategy profiles of others. A strategy is iteratively TTD (i-TTD) if any iterate is TTD and payoff improving. We show that any mechanism only with undominated equilibria is not i-TTD manipulable. We also show that any TTD shill-bidding strategy is i-TTD. The Vickrey-Clarke-Groves (VCG) mechanism is not shill-proof, but neither the existence nor the nonexistence of TTD strategy had previously been known. We show both that VCG is TTD manipulable when externalities exist, but not TTD manipulable in package auctions without externalities.

Tight Revenue Gaps Among Simple Mechanisms

We consider a fundamental problem in microeconomics: selling a single item to a number of potential buyers, whose values are drawn from known independent and regular (not necessarily identical) distributions. There are four widely used and widely studied mechanisms in the literature: Myerson Auction (OPT), Sequential Posted-Pricing (SPM), Second-Price Auction with Anonymous Reserve (AR), and Anonymous Pricing (AP). OPT is revenue-optimal but complicated and also experiences several issues in practice such as fairness; AP is the simplest mechanism but also generates the lowest revenue among these four mechanisms; SPM and AR are of intermediate complexity and revenue. We explore revenue gaps among these mechanisms, each of which is defined as the largest ratio between revenues from a pair of mechanisms. We establish two tight bounds and one tighter bound: 1. SPM vs. AP: this ratio studies the power of discrimination in pricing schemes. We obtain the tight ratio of constant ${\cal{C}}^* \approx {2.62}$, closing the gap between $[\frac{e}{e - 1}, e]$ left before. 2. AR vs. AP: this ratio measures the relative power of auction scheme vs. pricing scheme, when no discrimination is allowed. We attain the tight ratio of $\frac{\pi^2}{6} \approx 1.64$, closing the previously known bounds $[\frac{e}{e - 1}, e]$. 3. OPT vs. AR: this ratio quantifies the power of discrimination in auction schemes and is previously known to be somewhere between [2, e]. The lower bound of 2 was conjectured to be tight by Hartline and Roughgarden [Proceedings of the 10th ACM Conference on Electronic Commerce, 2009, pp. 225--234] and Alaei et al. [Games Econom. Behav., 118 (2019), pp. 494--510]. We acquire a better lower bound of 2.15 and thus disprove this conjecture.

Auctions with Signaling Concerns

We study a symmetric private value auction with signaling, in which the auction outcome is used by an outside observer to infer the bidders' types. We elicit conditions under which an essentially unique D1 equilibrium bidding function exists in four auction formats: first-price, second-price, all-pay and the English auction. We obtain a strict ranking in terms of expected revenues: the first-price and all-pay auctions dominate the English auction but are dominated by the second-price auction.