A Generalized Vickrey Auction

In auction environments where bidders have pure private values, the Vickrey auction (Vickrey, 1961) provides a simple mechanism for efficiently allocating homogeneous goods. However, in environments where bidders have interdependent values, the Vickrey auction does not generally yield efficiency. This manuscript defines a "generalized Vickrey auction" which yields efficiency when bidders have interdependent values. Each bidder reports her type to the auctioneer. Given the reports, the auctioneer determines the allocation that maximizes surplus. The payment rule is the following extension of Vickrey auction pricing: a bidder is charged for a given unit that she wins according to valuations evaluated at the minimum signal that she could have reported and still won that unit.

An Ascending-Price Generalized Vickrey Auction

A simple characterization of the equilibrium conditions required to compute Vickrey payments in the Combinatorial Allocation Problem leads to an ascending price Generalized Vickrey Auction. The ascending auc- tion, iBundle Extend & Adjust (iBEA), maintains non-linear and perhaps non-anonymous prices on bundles of items, and terminates with the ef- cient allocation and the Vickrey payments in ex post Nash equilibrium. Crucially, iBEA is able to implement the Vickrey outcome even when the Vickrey payments are not supported in a single competitive equilibrium. The auction closes with Universal competitive equilibrium prices, which provide enough information to compute individualized discounts to adjust the nal prices and implement Vickrey payments.Engineering and Applied Science

An Iterative Generalized Vickrey Auction: Strategy-Proofness without Complete Revelation

The generalized Vickrey auction (GVA) is a strategy-proof combinatorial auction, in which truthful bidding is the optimal strategy for an agent. In this paper we address a fundamental problem with the GVA, which is that it requires agents to compute and reveal their values for all combinations of items. This can be very difficult for bounded-rational agents with limited or costly computation. We propose an experimental design for an iterative combinatorial auction. We have a theoretical proof that the the auction implements the outcome of the Vickrey auction in special cases, and initial experimental results support our conjecture that the auction implements the outcome of the Vickrey auction in all cases. The auction has better information properties than the sealedbid GVA: in each round agents must only bid for the set of bundles that maximize their utility given current ask prices, which does not require agents to compute their exact values for every bundle.Engineering and Applied Science

Efficient Auction-Based Grid Reservation using Dynamic Programming

Abstract — Auction mechanisms have been proposed as a means to efficiently and fairly schedule jobs in high-performance computing environments. The Generalized Vickrey Auction has long been known to produce efficient allocations while exposing users to truth-revealing incentives, but the algorithms used to compute its payments can be computationally intractable. In this paper we present a novel implementation of the Generalized Vickrey Auction that uses dynamic programming to schedule jobs and compute payments in pseudo-polynomial time. Additionally, we have built a version of the PBS scheduler that uses this algorithm to schedule jobs, and in this paper we present the results of our tests using this scheduler. I

Multi-Unit Auctions to Allocate Water Scarcity Simulating Bidding Behaviour with Agent Based Models

Multi-unit auctions are promising mechanisms for the reallocation of water. The main advantage of such auctions is to avoid the lumpy bid issue. However, there is great uncertainty about the best auction formats when multi-unit auctions are used. The theory can only supply the structural properties of equilibrium strategies and the multiplicity of equilibria makes comparisons across auction formats difficult. Empirical studies and experiments have improved our knowledge of multi- unit auctions but they remain scarce and most experiments are restricted to two bidders and two units. Moreover, they demonstrate that bidders have limited rationality and learn through experience. This paper constructs an agent-based model of bidders to compare the performance of alternative auction formats under circumstances where bidders submit continuous bid supply functions and learn over time to adjust their bids to improve their net incomes. We demonstrate that under the generalized Vickrey, simulated bids converge towards truthful bids as predicted by the theory and that bid shading is the rule for the uniform and discriminatory auctions. Our study allows us to assess the potential gains from agent-based modelling approaches in the assessment of the dynamic performance of multi-unit procurement auctions. Some recommendations on the desirable format of water auctions are provided.Multi-unit auctions, Learning, Multi-agent models, Water allocation

A note on the efficiency of position mechanisms with budget constraints

We study the social efficiency of several well-known mechanisms for the allocation of a set of available (advertising) positions to a set of competing budget-constrained users (advertisers). Specifically, we focus on the Generalized Second Price auction (GSP), the Vickrey–Clarke–Groves mechanism (VCG) and the Expressive Generalized First Price auction (EGFP). Using liquid welfare as our efficiency benchmark, we prove a tight bound of 2 on the liquid price of anarchy and stability of these mechanisms for pure Nash equilibria

Ex post implementation in environments with private goods

We prove by construction that ex post incentive compatible mechanisms exist in a private goods setting with multi-dimensional signals and interdependent values. The mechanism shares features with the generalized Vickrey auction of one-dimensional signal models. The construction implies that for environments with private goods, informational externalities (i.e., interdependent values) are compatible with ex post equilibrium in the presence of multi-dimensional signals.Ex post incentive compatibility, multi-dimensional information, interdependent values

Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords

We investigate the "generalized second price" auction (GSP), a new mechanism which is used by search engines to sell online advertising that most Internet users encounter daily. GSP is tailored to its unique environment, and neither the mechanism nor the environment have previously been studied in the mechanism design literature. Although GSP looks similar to the Vickrey-Clarke-Groves (VCG) mechanism, its properties are very different. In particular, unlike the VCG mechanism, GSP generally does not have an equilibrium in dominant strategies, and truth-telling is not an equilibrium of GSP. To analyze the properties of GSP in a dynamic environment, we describe the generalized English auction that corresponds to the GSP and show that it has a unique equilibrium. This is an ex post equilibrium that results in the same payoffs to all players as the dominant strategy equilibrium of VCG.