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We study a pricing and allocation problem of a seller of multiple units of a homogeneous item, and present a semi-market mechanism in the form of an iterative ascending-bid auction. The auction elicits buyers' preferences over a set of options offered by the seller, and processes them with a random-priority assignment scheme to address buyers' "fairness" expectations. The auction's termination criterion is derived from a mixed-integer programming formulation of the preference-based capacity allocation problem. We show that the random priority- and preference-based assignment policy is a universally truthful mechanism which can also achieve a Pareto-efficient Nash equilibrium. Computational results demonstrate that the auction mechanism can extract a substantial portion of the centralized system's profit, indicating its effectiveness for a seller who needs to operate under the "fairness" constraint., NA

Internet of Things (IoT) is a network of disparate objects enabled to exchange data with each other to implement smart applications. In near future, the possibility of a truly global IoT is expected to be covered by connecting billions of devices through emerging wireless systems such as the fifth generation of cellular networks (5G). Employing enhanced multiple access technologies and providing effective resource allocation schemes to maximize the number of supported devices is a highly important factor to make future networks practical. Most of the current researches consider Orthogonal Multiple Access (OMA) techniques and try to improve Quality of Service (QoS) metrics like the data rate. In this work, we investigate the problem of allocating resources in an uplink MC CDMA wireless IoT network, including channel assignment and power control, to satisfy the signal-to-interference ratio (SIR) requirement of all devices in a scalable manner. The problem is primarily formulated as a Mixed Integer Linear Programming (MILP) problem with the goal of maximizing the number of supported devices while the sum of transmit powers is minimized. We prove that the problem is NP-Hard in general, and use the Lagrangian relaxation and decomposition methods to provide a subgradient-based approach and find at least a near-optimal solution; yet in a homogeneous case where a same feasible SIR requirement and a same path gain are assumed for all devices, a closed-form solution is obtained. Towards an efficient solution for the general case, a centralized heuristic algorithm and an evolutionary distributed algorithm are developed. The distributed scheme consists of a Vickrey auction based channel assignment phase and a non-cooperative target SIR tracking power control phase to allocate resources in an iterative and decentralized manner. In the distributed scheme, the base station is not needed to know path gains. Numerical results show that the difference between the optimal solution and our proposed algorithms are negligible, so they can be efficiently employed in real-world scenarios.

A widespread claim in the auction literature about the most well known auction setting with i.i.d. private values is that the optimal reserve price for a second price auction is independent of the number n of bidders. This is indeed the case if the virtual valuation function is increasing, but this result fails to hold if the virtual valuation is non-monotone. In such case the optimal reserve price is weakly increasing in n and, as n tends to infinity, it tends to the highest regular valuation with zero virtual value.

Femtocells consisting of small femto base stations have emerged as an efficient solution for improving the capacity and coverage of wireless cellular networks. However, due to limited wireless radio resources, resource allocation is a key issue in two-tier femtocell networks. Motivated by this challenge, in this paper, we propose a resource allocation approach which satisfies the quality of service requirements and maximizes social welfare. Users compete with each other for a serving base station that fulfills their quality of service requirements, and the serving base stations prefer to serve more users to make more revenue. We model the competition among these rational decision makers as the Vickrey–Clarke–Groves auction game theory in which each user as a buyer submits a bid for resources, and each base station as a seller decides which users will win the auction and how much the winning users should pay and then it assigns the resources to the winning users. Unlike the previous studies, we also take into account macro user’s activity as cross-tier interference in the resource allocation process. We develop an algorithm based on Q-learning in which each user gradually learns from its own past information and adjusts its bid value to achieve the Nash equilibrium as the solution of the game without any interaction with other users. We also investigate the existence and uniqueness of the Nash equilibrium. Simulation results verify the accuracy of the numerical results obtained from the proposed model.

In spectrum auctions, bidders typically have synergistic values for combinations of licenses. This has been the key argument for the use of combinatorial auctions in the recent years. Considering synergistic valuations turns the allocation problem into a computationally hard optimization problem that generally cannot be approximated to a constant factor in polynomial time. Ascending auction designs such as the Simultaneous Multiple Round Auction (SMRA) and the single-stage or two-stage Combinatorial Clock Auction (CCA) can be seen as simple heuristic algorithms to solve this problem. Such heuristics do not necessarily compute the optimal solution, even if bidders are truthful. We study the average efficiency loss that can be attributed to the simplicity of the auction algorithm with different levels of synergies. Our simulations are based on realistic instances of bidder valuations we inferred from bid data from the 2014 Canadian 700 MHz auction. The goal of the paper is not to reproduce the results of the Canadian auction but rather to perform “out-of-sample” counterfactuals comparing SMRA and CCA under different synergy conditions when bidders maximize payoff in each round. With “linear” synergies, a bidder's marginal value for a license grows linearly with the total number of licenses won, while with the “extreme national” synergies, this marginal value is independent of the number of licenses won unless the bidder wins all licenses in a national package. We find that with the extreme national synergy model, the CCA is indeed more efficient than SMRA. However, for the more realistic case of linear synergies, SMRA outperforms various versions of CCA that have been implemented in the field including the one used in the Canadian 700 MHz auction. Overall, the efficiency loss of all ascending auction algorithms is small even with high synergies, which is remarkable given the simplicity of the algorithms.

Ausubel (2004) introduces a new ascending-bid auction rule for multiple homogeneous objects, called the Ausubel auction, which is a dynamic counterpart of the Vickrey auction. He claims that in the Ausubel auction with private values, sincere bidding by all bidders is an ex post perfect equilibrium. However, we show that this claim does not hold in general by providing a counterexample. We then modify the Ausubel auction so that sincere bidding by all bidders is an ex post perfect equilibrium. (JEL D44)

One of the most important results in auction theory is that when bidders are symmetric (homogeneous), then under quite general conditions, the seller's expected revenue is independent of the auctio...

The paper empirically studies why the sellers of identical commodities adopt different auction formats in the online auction, and the consequences thereof. We postulate that the sellers adopt different auction formats because of the differences in their experience and the number of items they have. We first use these two characteristics to endogeneize the seller's choice between three auction formats: fixed-price, buy-it-now (BIN), and pure auctions. We then estimate the differences in sales rate, transaction price, and sale duration between the three formats. We find that the fixed-price auction results in the highest transaction price and the lowest sale rate, while the pure auction is just the opposite, with the BIN auction falling in between. These results strongly suggest that there is a tradeoff between price and sale probability in adopting different formats of auctions.

Little is known about the value of sustainably-produced rice and incentive mechanisms for the adoption of sustainable production standards throughout rice value chains in Southeast Asia. This study tests the feasibility of a market-based incentive mechanism by eliciting consumers’ willingness-to-pay (WTP) for rice produced and labeled under a national sustainable production standard in the South of Vietnam through experimental auctions. Domestic consumers are willing to pay a 9% price premium for certified sustainably-produced rice. This premium gradually increases up to 33% when incremental levels of information on certification and traceability are provided. Consumers willing to pay premiums for sustainably-produced rice are more health-conscious, have better knowledge of and greater trust in food quality certification for rice, and tend to be more environmentally conscious and to read food labels before purchasing. Findings suggest that sustainable production labels for rice should be accompanied by supplementary information on certification and traceability to increase consumers’ awareness and appreciation of sustainably-produced rice. Promoting certified sustainably-produced rice hence crucially hinges on strengthening consumers’ knowledge of and trust in food quality certification. Communication strategies are recommended to focus on the environmental and health benefits of sustainably-produced rice.

We study the effect of prebidding in first-price auctions with a single prize under incomplete information. The values of the n − 1 bidders are private information while bidder 1’s value is commonly known. Bidder 1 places his bid before all the n − 1 bidders. We show that regardless of his value, bidder 1 always has a positive effect on the expected highest bid. However, bidder 1’s contribution to the expected highest bid is not significant since the prebidding first-price auction with n bidders may be less profitable than the optimal simultaneous first-price auction with only n − 1 bidders. On the other hand, by giving the optimal head start to bidder 1, the prebidding first-price auction is always more profitable than the optimal simultaneous first-price auction with n − 1 bidders

We analyze bidding data from uniform price auctions of US Treasury bills and notes between July 2009 and October 2013. Primary dealers consistently bid higher yields compared to direct and indirect bidders. We estimate a structural model of bidding that takes into account informational asymmetries introduced by the bidding system employed by the US Treasury. While primary dealers' estimated willingness-to-pay is higher than direct and indirect bidders’, their ability to bid-shade is even higher, leading to higher yield/lower price bids. Total bidder surplus averaged to about three basis points across the sample period along with efficiency losses around two basis points. (JEL D44, E63, H63)

Evidence suggests that people evaluate outcomes relative to expectations. I analyze this expectations-based loss aversion a la Kőszegi and Rabin in the context of dynamic and static auctions, where the reference point is given by the (endogenous) equilibrium outcome. If agents update their reference point during the auction, the arrival of information crucially affects equilibrium behavior. Consequently, I show that—even with independent private values—the Vickrey auction yields strictly higher revenue than the (ascending clock) English auction, violating the well-known revenue equivalence.

Economists generally believe that more choice is beneficial, yet bigger choice sets can impose opportunity, error and cognitive costs that lower demand. We study this relationship in the context of rural energy use in low-income settings. We invited approximately 1100 randomly selected Senegalese households to participate in second-price auctions for improved cookstoves, and exogenously varied the number and types of devices being auctioned to identify the causal impact of expanded choice on willingness to pay (WTP). Expanded choice lowered WTP for a more advanced but relatively unfamiliar cookstove by 25%, but had no effect on WTP for a simpler, locally produced device. Households’ ability to compare alternatives side-by-side during multi-device auctions and identify the one best suited to their needs appears to drive these results. Our findings have implications for the design of policies that aim to introduce welfare-improving technologies in remote, rural areas.

This study examines asymmetric wheat auctions, with an object that is indivisible at the bidding stage, but divisible at the resale stage. Two bidders compete on auction. One is a large-sized miller, who can process the object being auctioned, and the other is a small-sized miller, who can only process part of the object. We show that this auction has a monotone equilibrium, and that the seller’s expected revenue in the second-price auction is strictly larger than that in the first-price auction. Moreover, we develop a threshold as a criterion for the small-sized miller’s speculating behavior on auction.

Companies that provide service at geographically dispersed locations face the problem of determining the technician that will serve each location as well as setting the best route for each technician. Such a scenario is known as the field service routing problem. Large companies often outsource their field service tasks to several contractors. Each contractor may serve several companies. Since the contractors cannot share the information about the tasks of their other clients, the most common practice involves allocating the tasks to the contractors heuristically based on geographical considerations. In this approach, the tasks for which the contractors have already been committed to other companies are not considered. As a result, the allocation of new tasks can be inefficient. This study develops 2-stage task allocation mechanisms that cope with the problem and result in nearly optimal allocations. In the first stage, a feasible allocation of tasks to contractors is generated. We consider two possible allocation procedures: sequential combinatorial auctions and sequential negotiations. The sequential combinatorial auctions procedure implements the Generalized Vickrey auction, which is a strategy-proof mechanism for the allocation of multiple goods among several competing agents. A sequential negotiation method is suggested as an alternative task allocation mechanism. The method automates a multi-lateral negotiation process in which the company is the leader, and the contractors are followers. In the second stage, the contractors are allowed to exchange the tasks among themselves so as to decrease their operational costs. The exchanges may or may not include money transfers. We found that the first-stage procedures yield fairly efficient allocations and the second stage further improves them. The obtained allocations are considerably more efficient than the solutions generated by a reasonable benchmark heuristic. Moreover, the allocations' costs are close to a lower bound established by the optimal allocation of a central planner. That is, the price of decentralization is shown to be small.

Several studies show that sensory cues influence consumer decision making processes. While scent is a key component of a market’s physical environment, it has received far less attention in the academic literature as compared, for example, with visual cues. In addition, most of the studies that examine the effect of ambient scents fail on one or both of these criteria: to properly control the influence of nuisance factors and/or to elicit preferences under real monetary incentives. We collected data from a laboratory experiment where we varied on a between subjects design the dispersion of a citrus fragrance. We then elicited subjects’ willingness to pay for two unbranded products — a mug and a chocolate — by having subjects participate in a 2nd price Vickrey auction. We also elicited subjects’ risk preferences using lottery choice tasks. Our results show a statistically and economically significant effect on subjects’ willingness to pay: valuations increased up to 49% for subjects who were exposed to a citrus scent as compared to the control group. We do not find a statistically significant effect of the citrus scent on subjects’ risk aversion.

In the private values single object auction model, we construct a satisfactory mechanism—a dominant strategy incentive compatible and budget-balanced mechanism satisfying equal treatment of equals. Our mechanism allocates the object with positive probability to only those agents who have the highest value and satisfies ex-post individual rationality. This probability is at least $$(1-\frac{2}{n})$$ , where n is the number of agents. Hence, our mechanism converges to efficiency at a linear rate as the number of agents grow. Our mechanism has a simple interpretation: a fixed allocation probability is allocated using a second-price Vickrey auction whose revenue is redistributed among all the agents in a simple way. We show that our mechanism maximizes utilitarian welfare among all satisfactory mechanisms that allocate the object only to the highest-valued agents.

Participation in internet auctions goes well beyond those who place a bid. Participants arrive in random order, and if the auction’s standing price has already exceeded a participant’s valuation, she will not bid. Even so, her unreported valuation is a relevant part of demand for the item, and in an alternate random order, her bid would have been registered. I provide a method to estimate the average number of participants from the average number of bidders per auction. This enables estimation of the distribution of participant valuations from either the distribution of closing prices or the distribution of all observed bids.

This paper studies bidding behavior in a dynamic auction setting that is similar to auctions offered on the Internet. I allow bidders to acquire outside prices while the auction is in progress. Searching is costly and bidders are heterogeneous in their search costs. The model generates a tractable equilibrium and gives interpretation to three intuitive bidding patterns that are frequently observed in the data: early, late and multiple bidding. The key feature of the equilibrium is that early bidding is monotone in search cost which leads to efficient sorting.

This paper studies the extent to which equilibrium auction prices are affected by the order of sale and the extent of product differentiation in the context of government land auction sales. We propose a simple two-stage differentiated duopoly model where an incumbent winner of land from a previous auction bids on a new piece of land with the anticipation of competition between developed properties on both land parcels. Our simple model suggests that the closer substitutes both plots of land are, the more likely that the incumbent will bid higher. The model also predicts that the incumbent will bid higher than the winning price of the previous parcel, but may not necessarily win the bid. Using a unique dataset that covers the universe of tendering prices submitted by all developers for all residential land auction sales in Singapore, we test this theory and find that a tenderer’s bids are higher where there was a previous piece of land sold within two years and located within four kilometers. The price margin decreases with distance and time. Moreover, by comparing the sequential bidding behavior of the incumbent and the second highest bidder with slightly lower bid, we show that the incumbent is more likely to participate in subsequent auction sales, especially for closer sites. The evidence on winning the same site is insignificant, consistent with our model predictions.

Sponsored Search Auctions (SSAs) are one of the most successful applications of microeconomic mechanisms, with a revenue of about $72 billion in the US alone in 2016. However, the problem of designing the best economic mechanism for sponsored search auctions is far from being solved, and, given the amount at stake, it is no surprise that it has received growing attention over the past few years. The most common auction mechanism for SSAs is the Generalized Second Price (GSP). However, the GSP is known not to be truthful: the agents participating in the auction might have an incentive to report false values, generating economic inefficiency and suboptimal revenues in turn. Superior, efficient truthful mechanisms, such as the Vickrey-Clarke-Groves (VCG) auction, are well known in the literature. However, while the VCG auction is currently adopted for the strictly related scenario of contextual advertising, e.g., by Google and Facebook, companies are reluctant to extend it to SSAs, fearing prohibitive switching costs. Other than truthfulness, two issues are of paramount importance in designing effective SSAs. First, the choice of the user model; not only does an accurate user model better target ads to users, it also is a critical factor in reducing the inefficiency of the mechanism. Often an antagonist to this, the second issue is the running time of the mechanism, given the performance pressure these mechanisms undertake in real-world applications. In our work, we argue in favor of adopting the VCG mechanism based on the cascade model with ad/position externalities (APDC-VCG). Our study includes both the derivation of inefficiency bounds and the design and the experimental evaluation of exact and approximate algorithms.

A multi-item auction is a situation in which one or several auctioneers propose a set of items and bidders exert effort for each item in an attempt to win a prize or an item. Multi-item lowest unique bid auction have been proposed recently in online platforms. Decision to participate or not is costly and left to the bidders. However, finding an optimal bidding strategy is not a trivial task because of incomplete information, heterogeneous valuation and budget restrictions. In this paper we examine the attitude of the bidders towards the risk. In contrast to risk-neutral agents who bids very small values, the cumulative distribution and the bidding support of risk-sensitive agents are more distributed.

In some markets bidders want to maximize value subject to a budget constraint rather than payoff. This is different to the quasilinear utility functions typically assumed in auction theory and leads to different strategies and outcomes. We refer to bidders who maximize value as value bidders. While simple single-object auction formats are truthful, standard multi-object auction formats allow for manipulation. It is straightforward to show that there cannot be a truthful and revenue-maximizing deterministic auction mechanism with value bidders and general valuations. Approximation has been used as remedy to achieve truthfulness on other mechanism design problems, and we study which approximation ratios we can get from truthful mechanisms. We show that the approximation ratio that can be achieved with a deterministic and truthful approximation mechanism with n bidders cannot be higher than 1/ n for general valuations. For randomized approximation mechanisms there is a framework with a ratio that is tight.

We model a spectrum auction where firms purchase units to participate in a constrained, multi-product, downstream market. We use dynamic programming techniques to numerically solve for the optimal bidding strategy in a clock auction. Firms value constraining competitor market power, so incumbents often bid aggressively to shut out entrants. We find that high cost firms may hold up the market, so the auction may be inefficient and generate zero revenue. An auction may be optimal for a regulator maximising total surplus. A regulator maximising auction revenue sets reserve prices high enough to restrict spectra sold, effectively behaving as a monopolist.

The Dutch auction, also known as the descending-price auction or reverse clock auction, has a long-standing history in practice and in academic literature. In practice, the Dutch auction is commonly used to rapidly sell large quantities of homogeneous goods, such as cut flowers, fish, or tobacco. However, most e-commerce auction sites focus on other auction mechanisms, and overall research on human behavior in Dutch auctions is scant. To facilitate research on Dutch auctions and their applications in electronic commerce, we conduct a structured literature review of experimental studies and establish the current state of research on bidding behavior in single-unit and multi-unit Dutch auctions. The findings are based on an analysis of twenty-nine articles published in the fields of economics, information management, marketing, and operations research and management science between 1970 and 2016. This review reveals (1) the characteristics that make the Dutch auction unique compared to other auction...

We extend the multi-item auction model of Talman and Yang (2008) and Andersson et al. (2015) by considering both unit-demand bidders with budget constraints and price controls on bidding items. Due to these budget and price restrictions, a Walrasian equilibrium generally fails to exist. To achieve efficiency, we propose a rationed equilibrium whose allocation is in the core. We also construct an ascending auction to find the proposed rationed equilibrium in (pseudo-)polynomial time.

The first spectrum auctions generally assigned the chosen number of licences of predetermined size to the highest bidders, but auctions now allow a greater choice of outcomes, with bidders with existing spectrum portfolios competing, with others, for multiple lots, often in different bands. Modern auctions also contain design features expressly directed at efficiency and equity objectives. In relation to efficiency, spectrum caps or set asides for new entrants can be incorporated to combat the exercise of market power downstream. In relation to equity objectives, licence conditions may specify obligations to provide coverage in non-commercial areas, or promises of the attainment of social objectives can be given a weighting, with revenue, in the determination of winning bids. The paper provides and overview of the wide use of such tools and the consequences for the operation of the auction process. Some lessons are drawn for future spectrum auctions.

Germany was the first country in Europe that auctioned off spectrum in the valuable 700 MHz band for mobile telecommunication usage. The German regulator decided to sell this spectrum together with spectrum in the 900 MHz and 1800 MHz legacy bands. With only the three incumbent operators bidding in the auction and a relatively transparent auction design, it was possible to get a very clear impression of the actual bidding behaviour. We show that in the beginning of the auction, bidders were actively searching for a way to allocate the available spectrum that all bidders could agree to at low prices. Bidders were teaching each other what they should bid and were providing carrots and sticks. When the excess demand was concentrated in one band only, bidders started to compete head on leading to a war of attrition. This competition only stopped when bidders started to raise prices in bands that were already cleared. We interpret this bidding behaviour in terms of bidders expressing allocative externalities and conclude that the ability to do so may be regarded as a positive aspect of the transparent design.

This article proposes a unified framework to completely characterize the seller's optimal listing strategy in the online auction as a function of her rate of time impatience. Specifically, the fixed‐price listing, the regular auction, and the buy‐it‐now (BIN) auction are each a solution of the seller's single optimization problem under different values of the rate of intertemporal discount: The perfectly patient seller adopts the regular auction, the sellers with a medium range of time impatience adopt the BIN auction, and the most impatient of sellers adopt the fixed‐price listing. Moreover, under mild conditions, the reverse price is inversely related to the value of the seller's discount factor, either within or across formats. This in turn implies that the posted price in the fixed‐price sale is greater than the reserve price of the BIN auction, followed by that of the regular auction. These predictions offer clear empirical implications.

By incorporating platform fees and bidders’ stochastic arrival process into the analysis of the multi-unit Vickrey auctions, we examine the performance of the two popular selling mechanisms (posted price and auction) on the Internet, characterize and derive the closed-form solution for the optimal lot-sizing policies. We show that the seller prefers auctions rather than posted price selling only when the valuation dispersion and the Web traffic are both sufficiently large. The theory also implies that there is no dominant selling mechanism. Since it is not always beneficial for the seller to auction more goods in a single auction, we further derive the optimal number of auction the seller should run and the optimal number of units to be sold in each auction. Moreover, we consider how to reconcile the conflict interests between the seller and the auction platform in single period and multi-period auctions respectively. Our main results indicate that, to decrease the listing fees, increase commission ratio and shorten the auction duration are all helpful for the platform to coordinate its interests with that of the seller.

Cloud computing is able to allocate different resources as virtual machines (VMs) to users, who need only pay for the amount of resources used. Two of the challenges in clouds are resource allocation and pricing in such a way to satisfy both cloud providers and users. Existing allocation and pricing mechanisms cannot guarantee increased profits due to various reasons. A better solution to increase the satisfaction of both parties, which is supported by economic theory, is the employment of auction-based allocation and pricing mechanisms. In these mechanisms, cloud resources and services are awarded based on the highest bids, while winners receive the quality of services expected. However, most existing auction-based mechanisms are inefficient and cannot be used in real clouds due to high computational or communication overhead, the bid function’s time complexity, and/or its inaccurate estimates. In the present paper, a lightweight mechanism is introduced which can be utilized in the real-world application of clouds. The currently proposed mechanism is a winner-bid auction game that seals users’ bids by a multi-criteria valuation-based bid function and sends them to the auctioneer. During scheduling, the auctioneer awards VMs exclusively to users with the highest bids. The presented approach is an online auction whose main aim is to increase the profits of the provider and user from different criteria. While determining the Nash equilibrium, the current study specifies the prices to be paid by users in various cases and proves the truthfulness of the proposed method. Finally, the effectiveness of the presented mechanism is examined through extensive experiments on different simulation scenarios and actual workload data.