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.

GAF: A General Auction Framework for Secure Combinatorial Auctions

<p>Auctions are an economic mechanism for allocating goods to interested parties. There are many methods, each of which is an Auction Protocol. Some protocols are relatively simple such as English and Dutch auctions, but there are also more complicated auctions, for example combinatorial auctions which sell multiple goods at a time, and secure auctions which incorporate security solutions. Corresponding to the large number of protocols, there is a variety of purposes for which protocols are used. Each protocol has different properties and they differ between how applicable they are to a particular domain. In this thesis, the protocols explored are privacy preserving secure combinatorial auctions which are particularly well suited to our target domain of computational grid system resource allocation. In grid resource allocation systems, goods are best sold in sets as bidders value different sets of goods differently. For example, when purchasing CPU cycles, memory is also required but a bidder may additionally require network bandwidth. In untrusted distributed systems such as a publicly accessible grid, security properties are paramount. The type of secure combinatorial auction protocols explored in this thesis are privacy preserving protocols which hide the bid values of losing bidder’s bids. These protocols allow bidders to place bids without fear of private information being leaked. With the large number of permutations of different protocols and configurations, it is difficult to manage the idiosyncrasies of many different protocol implementations within an individual application. This thesis proposes a specification, design, and implementation for a General Auction Framework (GAF). GAF provides a consistent method of implementing different types of auction protocols from the standard English auction through to the more complicated combinatorial and secure auctions. The benefit of using GAF is the ability to easily leverage multiple protocols within a single application due to the consistent specification of protocol construction. The framework has be tested with three different protocols: the Secure Polynomial auction protocol, the Secure Homomorphic auction protocol and the Secure Garbled Circuits auction protocol. These three protocols and a statistics collecting application is a proof of concept for the framework and provides the beginning of an analysis designed at determining suitable protocol candidates for grid systems.</p>

GAF: A General Auction Framework for Secure Combinatorial Auctions

<p>Auctions are an economic mechanism for allocating goods to interested parties. There are many methods, each of which is an Auction Protocol. Some protocols are relatively simple such as English and Dutch auctions, but there are also more complicated auctions, for example combinatorial auctions which sell multiple goods at a time, and secure auctions which incorporate security solutions. Corresponding to the large number of protocols, there is a variety of purposes for which protocols are used. Each protocol has different properties and they differ between how applicable they are to a particular domain. In this thesis, the protocols explored are privacy preserving secure combinatorial auctions which are particularly well suited to our target domain of computational grid system resource allocation. In grid resource allocation systems, goods are best sold in sets as bidders value different sets of goods differently. For example, when purchasing CPU cycles, memory is also required but a bidder may additionally require network bandwidth. In untrusted distributed systems such as a publicly accessible grid, security properties are paramount. The type of secure combinatorial auction protocols explored in this thesis are privacy preserving protocols which hide the bid values of losing bidder’s bids. These protocols allow bidders to place bids without fear of private information being leaked. With the large number of permutations of different protocols and configurations, it is difficult to manage the idiosyncrasies of many different protocol implementations within an individual application. This thesis proposes a specification, design, and implementation for a General Auction Framework (GAF). GAF provides a consistent method of implementing different types of auction protocols from the standard English auction through to the more complicated combinatorial and secure auctions. The benefit of using GAF is the ability to easily leverage multiple protocols within a single application due to the consistent specification of protocol construction. The framework has be tested with three different protocols: the Secure Polynomial auction protocol, the Secure Homomorphic auction protocol and the Secure Garbled Circuits auction protocol. These three protocols and a statistics collecting application is a proof of concept for the framework and provides the beginning of an analysis designed at determining suitable protocol candidates for grid systems.</p>

Verifying Privacy Preserving Combinatorial Auctions

<p>Suppose you are competing in an online sealed bid auction for some goods. How do you know the auction result can be trusted? The auction site could be performing actions that support its own commercial interests by blocking certain bidders or even reporting incorrect winning prices. This problem is magnified when the auctioneer is an unknown party and the auctions are for high value items. The incentive for the auctioneer to cheat can be high as they could stand to make a significant profit by inflating winning prices or by being paid by a certain bidder to announce them the winner. Verification of auction results provides confidence in the auction result by making it computationally infeasible for an auction participant to cheat and not get caught. This thesis examines the construction of verifiable privacy preserving combinatorial auction protocols. Two verifiable privacy preserving combinatorial auction protocols are produced by extending existing auction protocols.</p>

Verifying Privacy Preserving Combinatorial Auctions

<p>Suppose you are competing in an online sealed bid auction for some goods. How do you know the auction result can be trusted? The auction site could be performing actions that support its own commercial interests by blocking certain bidders or even reporting incorrect winning prices. This problem is magnified when the auctioneer is an unknown party and the auctions are for high value items. The incentive for the auctioneer to cheat can be high as they could stand to make a significant profit by inflating winning prices or by being paid by a certain bidder to announce them the winner. Verification of auction results provides confidence in the auction result by making it computationally infeasible for an auction participant to cheat and not get caught. This thesis examines the construction of verifiable privacy preserving combinatorial auction protocols. Two verifiable privacy preserving combinatorial auction protocols are produced by extending existing auction protocols.</p>

A Graph-Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions

Iterative combinatorial auctions are known to resolve bidder preference elicitation problems. However, winner determination is a known key bottleneck that has prevented widespread adoption of such auctions, and adding a time-bound to winner determination further complicates the mechanism. As a result, heuristic-based methods have enjoyed an increase in applicability. We add to the growing body of work in heuristic-based winner determination by proposing an ant colony metaheuristic–based anytime algorithm that produces optimal or near-optimal winner determination results within specified time. Our proposed algorithm resolves the speed versus accuracy problem and displays superior performance compared with 20 past state-of-the-art heuristics and two exact algorithms, for 94 open test auction instances that display a wide variety in bid-bundle composition. Furthermore, we contribute to the literature in two predominant ways: first, we represent the winner determination problem as one of finding the maximum weighted path on a directed cyclic graph; second, we improve upon existing ant colony heuristic–based exploration methods by implementing randomized pheromone updating and randomized graph pruning. Finally, to aid auction designers, we implement the anytime property of the algorithm, which allows auctioneers to stop the algorithm and return a valid solution to the winner determination problem even if it is interrupted before computation ends.

Competing Combinatorial Auctions

Combinatorial auctions are auctions in which bids can be submitted on sets of items, rather than just on individual items. These auctions are generally beneficial to both auctioneers and bidders, as they allow bidders to express their synergies for sets of items. In recent years, we have seen the advent of combinatorial auctions as well as the emergence of online market platforms with competing auctioneers. However, combinatorial auctions have largely been absent from these platforms. Our article provides an explanation for this absence by demonstrating that competition between auctioneers can reduce the attractiveness of offering combinatorial auctions. Specifically, we show that auctioneers can limit competitive pressure between themselves by allowing bids only on specific packages, where these packages differ between auctioneers. This results in market segmentation, which increases bidder competition, and consequently increases auctioneer revenues. These findings have implications for market design. In particular they imply that, for an online market platform having multiple sellers offering auctions to the same set of buyers, it might not be advantageous to offer combinatorial auctions as a design option to the competing sellers.