On the Efficiency of the Walrasian Mechanism

Central results in economics guarantee the existence of efficient equilibria for various classes of markets. An underlying assumption in early work is that agents are price-takers, i.e., agents honestly report their true demand in response to prices. A line of research in economics, initiated by Hurwicz (1972), is devoted to understanding how such markets perform when agents are strategic about their demands. This is captured by the \emph{Walrasian Mechanism} that proceeds by collecting reported demands, finding clearing prices in the \emph{reported} market via an ascending price t\^{a}tonnement procedure, and returns the resulting allocation. Similar mechanisms are used, for example, in the daily opening of the New York Stock Exchange and the call market for copper and gold in London. In practice, it is commonly observed that agents in such markets reduce their demand leading to behaviors resembling bargaining and to inefficient outcomes. We ask how inefficient the equilibria can be. Our main result is that the welfare of every pure Nash equilibrium of the Walrasian mechanism is at least one quarter of the optimal welfare, when players have gross substitute valuations and do not overbid. Previous analysis of the Walrasian mechanism have resorted to large market assumptions to show convergence to efficiency in the limit. Our result shows that approximate efficiency is guaranteed regardless of the size of the market

On the Economic Efficiency of the Combinatorial Clock Auction

Since the 1990s spectrum auctions have been implemented world-wide. This has provided for a practical examination of an assortment of auction mechanisms and, amongst these, two simultaneous ascending price auctions have proved to be extremely successful. These are the simultaneous multiround ascending auction (SMRA) and the combinatorial clock auction (CCA). It has long been known that, for certain classes of valuation functions, the SMRA provides good theoretical guarantees on social welfare. However, no such guarantees were known for the CCA. In this paper, we show that CCA does provide strong guarantees on social welfare provided the price increment and stopping rule are well-chosen. This is very surprising in that the choice of price increment has been used primarily to adjust auction duration and the stopping rule has attracted little attention. The main result is a polylogarithmic approximation guarantee for social welfare when the maximum number of items demanded $\mathcal{C}$ by a bidder is fixed. Specifically, we show that either the revenue of the CCA is at least an $\Omega\Big(\frac{1}{\mathcal{C}^{2}\log n\log^2m}\Big)$-fraction of the optimal welfare or the welfare of the CCA is at least an $\Omega\Big(\frac{1}{\log n}\Big)$-fraction of the optimal welfare, where $n$ is the number of bidders and $m$ is the number of items. As a corollary, the welfare ratio -- the worst case ratio between the social welfare of the optimum allocation and the social welfare of the CCA allocation -- is at most $O(\mathcal{C}^2 \cdot \log n \cdot \log^2 m)$. We emphasize that this latter result requires no assumption on bidders valuation functions. Finally, we prove that such a dependence on $\mathcal{C}$ is necessary. In particular, we show that the welfare ratio of the CCA is at least $\Omega \Big(\mathcal{C} \cdot \frac{\log m}{\log \log m}\Big)$

Online Auctions

The economic literature on online auctions is rapidly growing because of the enormous amount of freely available field data. Moreover, numerous innovations in auction-design features on platforms such as eBay have created excellent research opportunities. In this article, we survey the theoretical, empirical, and experimental research on bidder strategies (including the timing of bids and winner's-curse effects) and seller strategies (including reserve-price policies and the use of buy-now options) in online auctions, as well as some of the literature dealing with online-auction design (including stopping rules and multi-object pricing rules).

Measuring the Efficiency of an FCC Spectrum Auction

FCC spectrum auctions sell licenses to provide mobile phone service in designated geographic territories. We propose a method to structurally estimate the deterministic component of bidder valuations and apply it to the 1995–1996 C-block auction. We base our estimation of bidder values on a pairwise stability condition, which implies that two bidders cannot exchange licenses in a way that increases total surplus. Pairwise stability holds in many theoretical models of simultaneous ascending auctions, including some models of intimidatory collusion and demand reduction. Pairwise stability is also approximately satisfied in data that we examine from economic experiments. The lack of post-auction resale also suggests pairwise stability. Using our estimates of deterministic valuations, we measure the allocative efficiency of the C-block outcome.

Environmental analysis for application layer networks

Die zunehmende Vernetzung von Rechnern über das Internet lies die Vision von Application Layer Netzwerken aufkommen. Sie umfassen Overlay Netzwerke wie beispielsweise Peer-to-Peer Netzwerke und Grid Infrastrukturen unter Verwendung des TCP/IP Protokolls. Ihre gemeinsame Eigenschaft ist die redundante, verteilte Bereitstellung und der Zugang zu Daten-, Rechen- und Anwendungsdiensten, während sie die Heterogenität der Infrastruktur vor dem Nutzer verbergen. In dieser Arbeit werden die Anforderungen, die diese Netzwerke an ökonomische Allokationsmechanismen stellen, untersucht. Die Analyse erfolgt anhand eines Marktanalyseprozesses für einen zentralen Auktionsmechanismus und einen katallaktischen Markt. --Grid Computing

Auctions, Bidding and Exchange Design

The different auction types are outlined using a classification framework along six dimensions. The economic properties that are desired in the design of auction mechanisms and the complexities that arise in their implementation are discussed. Some of the most interesting designs from the literature are analyzed in detail to establish known results and to identify the emerging research directions.Engineering and Applied Science

Tight Bounds for the Price of Anarchy of Simultaneous First Price Auctions

We study the Price of Anarchy of simultaneous first-price auctions for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian Price of Anarchy of these auctions are e/(e-1) [Syrgkanis and Tardos 2013] and 2 [Feldman et al. 2013], respectively. We provide matching lower bounds for both cases even for the case of full information and for mixed Nash equilibria via an explicit construction. We present an alternative proof of the upper bound of e/(e-1) for first-price auctions with fractionally subadditive valuations which reveals the worst-case price distribution, that is used as a building block for the matching lower bound construction. We generalize our results to a general class of item bidding auctions that we call bid-dependent auctions (including first-price auctions and all-pay auctions) where the winner is always the highest bidder and each bidder's payment depends only on his own bid. Finally, we apply our techniques to discriminatory price multi-unit auctions. We complement the results of [de Keijzer et al. 2013] for the case of subadditive valuations, by providing a matching lower bound of 2. For the case of submodular valuations, we provide a lower bound of 1.109. For the same class of valuations, we were able to reproduce the upper bound of e/(e-1) using our non-smooth approach.Comment: 37 pages, 5 figures, ACM Transactions on Economics and Computatio

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