Multi-unit Auctions Research Articles

On incentivizing resource allocation and task offloading for cooperative edge computing

Cooperative edge computing serves as an effective solution to provide reliable and elastic edge computing services through pooling geographically proximate edge resources and efficiently allocating them to users. The incentive mechanism is critical for realizing cooperative edge computing. In this paper, we propose a virtual machine (VM) or container based resource allocation scheme and two market-based mechanisms to stimulate collaboration among edge servers (ESs). Our first mechanism is a novel two-stage double auction based approach where edge resources are allocated to services/VMs at the first stage and then distributed among ESs at the second stage via a two-sided multi-unit auction. To make it more practical, we use markups to set the ask and bid prices for the participants in the market. Moreover, with the concept of virtual sellers and virtual buyers, we cast the multi-unit auction as single-unit one so that the auction becomes tractable. We further propose a price-based decentralized mechanism in case there is no central authority. With an appropriately constructed objective function, we formulate the resource allocation task as a network utility maximization (NUM) problem and leverage the dual-based decomposition theory for a distributed solution. We theoretically prove that both mechanisms guarantee properties such as budget balance and individual rationality for all ESs. Numerical studies with real-world dataset are presented to demonstrate the superior performance of our mechanisms over baselines.

A note on the impossibility of multi-unit auctions with budget-constrained bidders

A note on the impossibility of multi-unit auctions with budget-constrained bidders

Analysing different payment methods in multi-unit auctions: An empirical evidence from Delhi NCR India

Analysing different payment methods in multi-unit auctions: An empirical evidence from Delhi NCR India

Multi-Unit Auctions for Allocating Chance-Constrained Resources

Sharing scarce resources is a key challenge in multi-agent interaction, especially when individual agents are uncertain about their future consumption. We present a new auction mechanism for preallocating multi-unit resources among agents, while limiting the chance of resource violations. By planning for a chance constraint, we strike a balance between worst-case approaches, which under-utilise resources, and expected-case approaches, which lack formal guarantees. We also present an algorithm that allows agents to generate bids via multi-objective reasoning, which are then submitted to the auction. We then discuss how the auction can be extended to non-cooperative scenarios. Finally, we demonstrate empirically that our auction outperforms state-of-the-art techniques for chance-constrained multi-agent resource allocation in complex settings with up to hundreds of agents.

Walrasian pricing in multi-unit auctions

Multi-unit auctions are a paradigmatic model of resource allocation, where a seller brings multiple units of a good to a set of buyers equipped with monetary budgets. It is well known that Walrasian equilibria do not always exist in this model, however compelling relaxations such as Walrasian envy-free pricing do.We design a best possible envy-free and prior-free mechanism for multi-unit auctions with budgets. When the market is even mildly competitive, the approximation ratios of this mechanism are small constants for both the revenue and welfare objectives, and in fact for welfare the approximation converges to 1 as the market becomes fully competitive. We also give an impossibility theorem, showing that truthfulness requires discarding resources and is thus incompatible with (Pareto) efficiency.

The Price of Anarchy of Two-Buyer Sequential Multiunit Auctions

We study the efficiency of first-/second-price sequential multiunit auctions with two buyers and complete information. Extending the primal-dual framework for obtaining efficiency bounds to this sequential setting, we obtain tight price of anarchy bounds. For general valuation functions, we show that the price of anarchy is exactly 1/T for auctions with T items for sale. For concave valuation functions, we show that the price of anarchy is bounded below by 1-1/e≃ 0.632 . This bound is asymptotically tight as the number of items sold tends to infinity.

Characterization of incentive compatible single-parameter mechanisms revisited<

We reexamine the characterization of incentive compatible single-parameter mechanisms introduced in Archer & Tardos (2001). We argue that the claimed uniqueness result, called 'Myerson's Lemma' was not well established. We provide an elementary proof of uniqueness that unifies the presentation for two classes of allocation functions used in the literature and show that the general case is a consequence of a little known result from the theory of real functions. We also clarify that our proof of uniqueness is more elementary than the previous one. Finally, by generalizing our characterization result to more dimensions, we provide alternative proofs of revenue equivalence results for multiunit auctions and combinatorial auctions.

Auctions with Privately Known Capacities: Understanding Competition Among Renewables

Abstract We study a multi-unit auction model in which bidders are privately informed about the maximum number of units they are willing to trade (which we refer to as ‘capacity’). No matter how big or small, private information on capacities changes the nature of the equilibrium as compared to when private information is on costs (or valuations). Also, the uniform-price and discriminatory auctions are not revenue equivalent, in contrast to when costs are independently drawn. In particular, with independently drawn capacities (and possibly costs), the discriminatory format reduces payments to firms relative to the uniform-price format. Our analysis is motivated by the performance of future electricity markets in which renewable energies will be predominant, but the set-up also applies to a variety of contexts (from central bank liquidity auctions to emissions trading).

Best of Both Worlds Ad Contracts: Guaranteed Allocation and Price with Programmatic Efficiency

Buying display ad impressions via real-time auctions comes with significant allocation and price uncertainties. We design and analyze a contract that mitigates this uncertainty risk by providing guaranteed allocation and prices while maintaining the efficiency of buying in an auction. We study how risk aversion affects the desire for guarantees and how to price a guaranteed allocation. We propose to augment the traditional auction with a programmatic purchase option (which we call a Market-Maker contract) that removes allocation and price uncertainties. Instead of participating in the auction, advertisers can secure impressions in advance at a fixed premium price offered by the Market-Maker. It is then the responsibility of the Market-Maker to procure these impressions by bidding in the auction. We model buyers as risk-averse agents and analyze the equilibrium outcome when buyers face two purchase options (auction and Market-Maker contract). We derive analytical expressions for the Market-Maker price that reveal insightful relationships with uncertainties in the auction price and buyers’ risk levels. We also show the existence of a Market-Maker price that simultaneously improves the seller’s revenue and the sum of buyers’ utilities. As a building block to our analysis, we establish the truthfulness of the multiunit auction when buyers have nonquasilinear utilities because of risk aversion. Recently, the Google’s Display & Video 360 platform started offering a product akin to Market-Maker called “Guaranteed Packages,” which was inspired by this paper. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Entry Deterrence and Collusion at Repeated Multiunit Auctions of ITQs

Entry Deterrence and Collusion at Repeated Multiunit Auctions of ITQs

Multi-Unit Auction in Social Networks with Budgets

We study multi-unit auctions in social networks, where each buyer has a fixed budget and can spread the sale information to the network neighbors. We design a mechanism encouraging buyers to report their valuations truthfully and spread the sale information. Our design uses the idea of the clinching mechanism to decide the transaction price and can be viewed as a network version of the mechanism. Most of the previous clinching mechanisms search for the transaction prices by increasing the current price. Our mechanism directly computes the transaction prices in polynomial time. Furthermore, the mechanism applies a technique to iteratively activate new buyers in the network. This ensures utility preservations of the buyers and benefits the seller. We prove key properties of our mechanism, such as no-positive-transfers, individual rationality, incentive compatibility, non-wastefulness and social welfare preservation.

Sovereign Debt Auctions in Turbulent Times

We use a model of multiunit discriminatory auctions with asymmetrically informed risk-averse bidders to analyze Mexican sovereign bond auctions during periods of macroeconomic stress. We argue that the discriminatory protocol provides insurance benefits to the government in bad times because it allows for uninformed bids above the marginal price to be executed at the bid price. Uninformed investors are willing to make such bids if the inframarginal risk premium is large enough to offset the winner's curse. In crisis periods, we infer 1 p.p. lower borrowing costs in the worst states of the world, but 2.2 p.p. higher average costs.

Designing Hybrid Mechanisms to Overcome Congestion in Sequential Dutch Auctions

A common problem in many mature markets is how to deal with congestion—a situation in which transaction requests from market participants cannot be accommodated in an expedited manner. This paper examines the congestion problem in sequential Dutch auction markets. Transactions in these markets typically involve perishable goods, making market clearing speed crucial. Traditionally, sequential Dutch auctions have been implemented with fast-paced auction clocks that process equally attractive bids in the order they arrive and only award the first bidder as the winner of each round, which can lead to serious congestion in case of a demand surge. We propose a hybrid mechanism that capitalizes on the discrete nature of the auction clock and batches together the highest bids, allowing multiple transactions at the same price in each round. To evaluate the performance of the hybrid mechanism, we first develop a game-theoretic model comparing the hybrid mechanism to the traditional sequential Dutch auction mechanism. Our model predicts that the hybrid mechanism will achieve higher operational efficiency without compromising allocative efficiency. We then complement the theoretical analysis by evaluating the hybrid mechanism through a quasi-natural field experiment. The empirical analysis of the field data shows that the hybrid mechanism can significantly speed up the market clearing process and increase price stability without affecting the expected revenue. Our findings shed new light on the design and operation of multi-unit auctions.

Bidder Support in Multi-item Multi-unit Continuous Combinatorial Auctions: A Unifying Theoretical Framework

Combinatorial auctions have seen limited applications in large-scale consumer-oriented marketplaces, partly due to the substantial complexity to keep track of auction status and formulate informed bidding strategies. We study the bidder support problem for the general multi-item multi-unit (MIMU) combinatorial auctions, where multiple heterogeneous items are being auctioned and multiple homogeneous units are available for each item. Under two prevalent bidding languages (OR bidding and XOR bidding), we derive theoretical results and design efficient algorithmic procedures to calculate important bidder support information, such as the winning bids of an auction and the minimum bidding value for a bid to win an auction either immediately or potentially in the future. Our results unify the theoretical insights on bidder support problem for different bidding languages as well as different special cases of general MIMU auctions, namely the single-item multi-unit (SIMU) auctions and the multi-item single-unit (MISU) auctions. We also consider auctions with additional bidding constraints, including batch-based combinatorial auctions and hierarchical combinatorial auctions, as well as the combinatorial reverse auctions, all of which have relevant practical applications (e.g., industrial procurements). Our results can be readily extended to solve the bidder support problems in these auction mechanisms.

Evaluating Auction Mechanisms for the Preservation of Cost-Aware Digital Objects under Constrained Digital Preservation Budgets

Digital preservation is a field of research focused on designing strategies for maintaining digital objects accessible for general use in the coming years. Out of the many approaches to digital preservation, the present research article is a continuation work of a previously published article containing a proposal for a novel object-centered paradigm to address the digital preservation problem where digital objects share part of the responsibility for self-preservation. In the new framework, the behavior of digital objects is modeled to find the best preservation strategy. The results presented in the current article add a new economic constraint to the object behavior. Now, differently from the previous paper, migrations, copies and updates are not free to use, but subject to budget limitations to ensure the economic sustainability of the whole preservation system, forcing the now-called cost-aware digital objects for efficient management of available budget. The presented approach compares two auction-based mechanisms, a multi-unit auction and a combinatorial auction, with a simple direct purchase strategy as possible efficient behaviors for budget management. TiM, a simulated environment for running distributed digital ecosystems, is used to perform the experiments. The simulated results map the relation between the studied purchase models with the sustained quality level of digital objects, as a measure of its accessibility, together with its budget management capabilities. About the results, the best performance corresponds to the combinatorial auction model. The results are a good approach to deal with the digital preservation problem from a sustainable point of view and open the door to future implementations with other purchase strategies.

Auctioning business licenses to engage in Cournot competition

We study auctions for business licenses, where only the winners can participate in Cournot competition. This is an example of a multi-unit auction with endogenous and interdependent values. We compare a pay-as-bid auction and a uniform price auction. Assuming that only the winners’ identity and their payments are announced after the auction, the former auction is advantageous in terms of auction revenue, and the latter is advantageous in terms of consumer surplus.

Renewable support and strategic pricing in electricity markets

We show how policies to support clean technologies change price competition and market outcomes. We present evidence from electricity markets, where regulators have implemented different policies to subsidize clean energy. Building on a multi-unit auction model, we show that currently applied subsidy designs either foster or attenuate competition. Contract-based output subsidies decrease firms’ mark-ups. In contrast, market-based designs that subsidize clean output via a regulatory premium on the market price lead to higher mark-ups. We confirm this finding empirically using auction data from the Spanish power market. Our empirical results show that the design choice for renewable subsidies significantly impacts pricing behavior of firms and policy costs for consumers.

A review of multiunit auctions with homogeneous goods

AbstractThis article provides a comprehensive survey of the literature on multiunit auctions with multiple homogeneous goods. Despite the importance of multiunit auctions, the research on these auctions attracted substantially less attention than single‐unit auctions. We start by providing a review of the theoretical literature on homogeneous good multiunit auctions where bidders have multiunit demands. The articles are categorized based on their models' assumptions regarding bidders' values and the type of auction. Furthermore, we review the empirical and experimental evidence related to these multiunit auctions to understand the relationship with the theoretical findings.

Polyhedral Clinching Auctions for Two-Sided Markets

In this paper, we present a new model and mechanisms for auctions in two-sided markets of buyers and sellers, where budget constraints are imposed on buyers. Our model incorporates polymatroidal environments and is applicable to a variety of models that include multiunit auctions, matching markets, and reservation exchange markets. Our mechanisms are built on the polymatroidal network flow model by Lawler and Martel. Additionally, they feature nice properties such as the incentive compatibility of buyers, individual rationality, Pareto optimality, and strong budget balance. The first mechanism is a two-sided generalization of the polyhedral clinching auction by Goel et al. for one-sided markets. The second mechanism is a reduce-to-recover algorithm that reduces the market to be one-sided, applies the polyhedral clinching auction by Goel et al., and lifts the resulting allocation to the original two-sided market via the polymatroidal network flow. Both mechanisms are implemented by polymatroid algorithms. We demonstrate how our framework is applied to the Internet display advertisement auctions.

Single-unit and multi-unit auction framework for peer-to-peer transactions

Peer-to-peer transactions appear in smart grids as a way to enable the direct transaction of energy among end-users (i.e., consumers, producers, and prosumers). This concept promotes the efficient use of local renewable energy sources among neighbours. Several studies proposed the application of peer-to-peer models for energy communities, microgrids, and aggregators to decrease energy costs for end-users and to promote the balance between consumption and generation. In this paper, it is proposed a framework to test, and validate, using a real environment, single- and multi-unit peer-to-peer auctions. It is also proposed six lightweight fully distributed peer-to-peer auction models, avoiding the need for a central operator. The lightweight of the proposed models enables their execution in the fog-computing layer using single-board computers deployed in end-users. The proposed framework, together with the proposed day-ahead models, was tested and validated in a real microgrid with five prosumers. The results of two weeks are discussed using a comparative economic analysis. The proposed framework and models were able to reduce energy costs for the end-users, promoting competitive free market behaviours, with multi-unit models outperforming single-unit models in the overall trading efficiency and monetary profits.