Preventing Strategic Manipulation in Iterative Auctions: Proxy Agents and Price-Adjustment

Iterative auctions have many computational advantages over sealed-bid auctions, but can present new possibilities for strategic manipulation. We propose a two-stage technique to make iterative auctions that compute optimal allocations with myopic best-response bidding strategies more robust to manipulation. First, introduce proxy bidding agents to constrain bidding strategies to (possibly untruthful) myopic bestresponse. Second, after the auction terminates adjust the prices towards those given in the Vickrey auction, a sealedbid auction in which truth-revelation is optimal. We present an application of this methodology to iBundle, an iterative combinatorial auction which gives optimal allocations for myopic best-response agents.Engineering and Applied Science

Characterization of the walrasian equilibria of the assignment model

We study the assignment model where a collection of indivisible goods are sold to a set of buyers who want to buy at most one good. We characterize the extreme and interior points of the set of Walrasian equilibrium price vectors for this model. Our characterizations are in terms of demand sets of buyers. Using these characterizations, we also give a unique characterization of the minimum and the maximum Walrasian equilibrium price vectors. Also, necessary and suncient conditions are given under which the interior of the set of Walrasian equilibrium price vectors is non-empty. Several of the results are derived by interpreting Walrasian equilibrium price vectors as potential functions of an appropriate directed graph.

Rate of Price Discovery in Iterative Combinatorial Auctions

We study a class of iterative combinatorial auctions which can be viewed as subgradient descent methods for the problem of pricing bundles to balance supply and demand. We provide concrete convergence rates for auctions in this class, bounding the number of auction rounds needed to reach clearing prices. Our analysis allows for a variety of pricing schemes, including item, bundle, and polynomial pricing, and the respective convergence rates confirm that more expressive pricing schemes come at the cost of slower convergence. We consider two models of bidder behavior. In the first model, bidders behave stochastically according to a random utility model, which includes standard best-response bidding as a special case. In the second model, bidders behave arbitrarily (even adversarially), and meaningful convergence relies on properly designed activity rules

Inefficiency of equilibria in query auctions with continuous valuations

Query auctions are iterative auctions in which bidders have to select in each round an action from a finite set. We show that, when bidders have continuous valuations, any ex post equilibrium in an ex post individually rational query auction can only be ex post efficient when the running time of the auction is infinite for almost all realizations of valuations of thebidders. Thus, when valuations are drawn from a continuous probability distribution, efficiency can only be bought at the expense of a running time that is infinite with probability one. For two bidders we even show this to be true when we only require efficiency with probability one.mathematical economics;

Overdemand and underdemand in economies with indivisible goods and unit demand

We study an economy where a collection of indivisible goods are sold to a set of buyers who want to buy at most one good. We characterize the set of Walrasian equilibrium price vectors in such an economy using sets of overdemanded and underdemanded goods. Further, we give characterizations for the minimum and the maximum Walrasian equilibrium price vectors of this economy. Using our characterizations, we give a suncient set of rules that generates a broad class of ascending and descending auctions in which truthful bidding is an ex post Nash equilibrium.

An Agent Based Market Design Methodology for Combinatorial Auctions

Auction mechanisms have attracted a great deal of interest and have been used in diverse e-marketplaces. In particular, combinatorial auctions have the potential to play an important role in electronic transactions. Therefore, diverse combinatorial auction market types have been proposed to satisfy market needs. These combinatorial auction types have diverse market characteristics, which require an effective market design approach. This study proposes a comprehensive and systematic market design methodology for combinatorial auctions based on three phases: market architecture design, auction rule design, and winner determination design. A market architecture design is for designing market architecture types by Backward Chain Reasoning. Auction rules design is to design transaction rules for auctions. The specific auction process type is identified by the Backward Chain Reasoning process. Winner determination design is about determining the decision model for selecting optimal bids and auctioneers. Optimization models are identified by Forward Chain Reasoning. Also, we propose an agent based combinatorial auction market design system using Backward and Forward Chain Reasoning. Then we illustrate a design process for the general n-bilateral combinatorial auction market. This study serves as a guideline for practical implementation of combinatorial auction markets design.Combinatorial Auction, Market Design Methodology, Market Architecture Design, Auction Rule Design, Winner Determination Design, Agent-Based System

Time bounds for iterative auctions : a unified approach by discrete convex analysis

We investigate an auction model where there are many different goods, each good has multiple units and bidders have gross substitutes valuations over the goods. We analyze the number of iterations in iterative auction algo- rithms for the model based on the theory of discrete convex analysis. By making use of L♮-convexity of the Lyapunov function we derive exact bounds on the number of iterations in terms of the ℓ1-distance between the initial price vector and the found equilibrium. Our results extend and unify the price adjustment algorithms for the multi-unit auction model and for the unit-demand auction model, offering computational complexity results for these algorithms, and reinforcing the connection between auction theory and discrete convex analysis

Multi-item Vickrey-Dutch auctions

Descending price auctions are adopted for goods that must be sold quickly and in private values environments, for instance in flower, fish, and tobacco auctions. In this paper, we introduce ex post efficient descending auctions for two environments: multiple non-identical items and buyers with unit-demand valuations; and multiple identical items and buyers with non-increasing marginal values. Our auctions are designed using the notion of universal competitive equilibrium (UCE) prices and they terminate with UCE prices, from which the Vickrey payments can be determined. For the unit-demand setting, our auction maintains linear and anonymous prices. For the homogeneous items setting, our auction maintains a single price and adopts Ausubel's notion of "clinching" to compute the final payments dynamically. The auctions support truthful bidding in an ex post Nash equilibrium and terminate with an ex post efficient allocation. In simulation, we illustrate the speed and elicitation advantages of these auctions over their ascending price counterparts.