Auction Problem Research Articles

Market‐Based Allocation with Indivisible Bids

We study multiunit double auctions accepting bids with indivisibility constraints. Modeling the auction problem as a Multiple Choice Knapsack Problem and using dynamic programming, we show that incremental computations during bid processing can speed the handling of key auction operations such as clearing and quoting. We propose different price‐quote policies and study their influence on the efficiency of market‐based allocation. Using a reconfigurable manufacturing scenario where agents trade large quantities of multiple goods, we demonstrate potential benefits of supporting indivisibility constraints in bidding. These benefits are highly sensitive to the form of price quote provided, indicating interesting tradeoffs in communication and allocation efficiency.

The participatory Vickrey–Clarke–Groves mechanism

This paper introduces the participatory Vickrey–Clarke–Groves mechanism, which satisfies both ex-ante budget balance and interim individual rationality. We bound the efficiency loss of this mechanism by a parameter that captures the structure of marginal contributions to the social welfare. We then apply the theory to quite general multiple unit double auction problems to show that the participatory VCG mechanism achieves asymptotic efficiency.

A market-based multi-agent system model for decentralized multi-project scheduling

We consider a multi-project scheduling problem, where each project is composed of a set of activities, with precedence relations, requiring specific amounts of local and shared (among projects) resources. The aim is to complete all the project activities, satisfying precedence and resource constraints, and minimizing each project schedule length. The decision making process is supposed to be decentralized, with as many local decision makers as the projects. A multi-agent system model, and an iterative combinatorial auction mechanism for the agent coordination are proposed. We provide a dynamic programming formulation for the combinatorial auction problem, and heuristic algorithms for both the combinatorial auction and the bidding process. An experimental analysis on the whole multi-agent system model is discussed.

Iterative Dutch combinatorial auctions

The combinatorial auction problem can be modeled as a weighted set packing problem. Similarly the reverse combinatorial auction can be modeled as a weighted set covering problem. We use the set packing and set covering formulations to suggest novel iterative Dutch auction algorithms for combinatorial auction problems. We use generalized Vickrey auctions (GVA) with reserve prices in each iteration. We prove the convergence of the algorithms and show that the solutions obtained using the algorithms lie within provable worst case bounds. We conduct numerical experiments to show that in general the solutions obtained using these algorithms are much better than the theoretical bounds.

Solving the combinatorial double auction problem

Abstract This paper studies the solution of several types of combinatorial (double) auctions. Such auctions have recently been used in business-to-business trading in a centralized marketplace, or in multi-agent coordination systems in artificial intelligence. When the goods are indivisible, solving the winner determination problem (WDP) is an integer programming problem and NP-hard in its general form. We show that a general combinatorial double auction can be reduced to a combinatorial single-sided auction, which is a multi-dimensional knapsack problem. Next, we compare the performance of several solution approaches for this type of problem. We contrast the branch-and-bound method with the intelligent search method proposed separately in three well-referenced papers. We found that theoretically the LP relaxation bounds always dominate the bounds used in the specialized intelligent searches. We also found empirically that the performance of this branch-and-bound method is superior to the specialized search methods that have been proposed for this class of problems.

COMBINATORIAL AUCTIONS MATHEMATICAL FORMULATIONS AND OPEN ISSUES

The widespread use of the Internet fostered the establishment of hundreds of sites that support on-line auctions of products and services, some of which also support combinatorial auctions. Finding the optimal combination of winning bids in combinatorial auctions is a difficult task. This paper presents the combinatorial auction problem, classifies combinatorial auctions by the different procedures used during the bidding process, presents some of the applications of combinatorial auctions, and develops mathematical models of combinatorial auctions. The mathematical models are used to identify some of the problem properties and prove that winner determination in combinatorial auctions has the same level of difficulty as solving the allocation problem facing an auctioneer. The paper concludes with the discussion on some of the complexities involved in combinatorial auctions.

Informational Size and Efficient Auctions

We develop an auction model for the case of interdependent values and multidimensional signals in which agents' signals are correlated. We provide conditions under which a modification of the Vickrey auction which includes payments to the bidders will result in an ex post efficient outcome. Furthermore, we provide a definition of informational size such that the necessary payments to bidders will be arbitrarily small if agents are sufficiently informationally small. The efficiency of market processes has been a central concern in economics since its inception. Auction mechanisms constitute a very important class of market processes, yet the analysis of auctions has typically focused on their revenue generating properties rather than their efficiency properties. This is partly due to the fact that, for many of the problems typically studied, efficiency is trivial. When bidders have private values, a standard Vickrey auction guarantees that the object will be sold to the buyer with the highest value for the object. In the case of pure common values-that is, when all buyers have the same value for the object-any outcome that with probability one assigns the object to some bidder will be efficient. The intermediate case in which bidders' values are not identical but may depend on other bidders' signals is more problematic. When bidders' values are interdependent in this way, any single bidder's value may depend on the information of other agents and, hence, he may not even know his own value. It is not clear what it would mean for an agent to bid his true value, even before we ask if it is optimal for him to do so. Several papers have studied efficient auctions with interdependent values and independent types.1 While this is a natural place to begin, the independence assumption is not compelling for many problems. A prototypical problem is one in which an object is to be sold, and individual bidders have private information about the object (say the quantity or quality of oil in a tract to be sold) that affects other agents' values for the object. When bidders' types include information about objective characteristics of the object being sold, their types will typically not be independent. When agents' types are statistically dependent, we show that there exist efficient auction mechanisms for interdependent value auction problems that are essentially Vickrey auctions augmented by payments to (not from) the agents. Most importantly, we link the

Optimal allocation of transmission rights in systems with FACTS devices

Financial transmission rights (FTR) is a market-based approach to transmission congestion management, which is essentially based on the locational marginal pricing (LMP) theory. FTR auction is an important method of allocating transmission capabilities to the market participants who value them most. A DC power flow model is applied to the FTR auction. To improve the result and the revenue of the FTR auction, two types of series FACTS devices are modelled as additional power injection at buses in the presented linear optimisation problem of FTR auction. Some new special treatments have been done on the TCSC operating limits to keep the auction problem linear. The impacts of controlling different FACTS devices on auction results are shown by detailed studies of an eight-bus test system and the IEEE 30-bus test system.

Weak and strong monotone comparative statics

This paper develops necessary and sufficient conditions for the set of solutions to an optimization problem to be nondecreasing in a weak sense still strong enough to guarantee the existence of an increasing selection, and thus strong enough to guarantee monotonicity when the solution is unique, as well as necessary and sufficient conditions for the set of optimizers to be nondecreasing in a strong sense which is strong enough to rule out the possibility of a decreasing selection. These necessary and sufficient conditions are variations of quasisupermodularity and the single crossing property introduced in Milgrom-Shannon [13]. Moreover, to determine when an objective function satisfies these conditions, this paper develops several characterizations of quasisupermodularity and the single crossing property and their variants, both in terms of differential conditions and in terms of restrictions on the structure of the level sets of these functions. Several examples are given to choice theory under loss aversion and to an auction problem.

Numerical Analysis of Asymmetric First Price Auctions

We propose numerical algorithms for solving first price auction problems where bidders draw independent valuations from heterogeneous distributions. The heterogeneity analyzed in this work is what might naturally emerge when subsets of distributionally homogeneous bidders collude. Bid functions and expected revenues are calculated for two special cases. Extensions to more general asymmetric first price auctions are discussed. Journal of Economic Literature Classification Numbers: D44, C63, C72, D82.

Asymptotic Efficiency in Large Exchange Economies With Asymmetric Information

The authors provide conditions on an exchange economy with asymmetric information that guarantee that when the economy is replicated sufficiently often, there will be an allocation that is incentive compatible, individually rational, and nearly efficient. The main theorem covers both the case in which aggregate uncertainty remains when the economy is replicated and the case in which replication eliminates aggregate uncertainty. In addition, the authors demonstrate how their theorem does or does not apply to standard asymmetric information problems such as the buyer's bid double auction problem, Akerlof's lemons problem, and insurance with asymmetric information. Copyright 1992 by The Econometric Society.