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When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…

We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a…

Using mechanised reasoning we prove that combinatorial Vickrey auctions are soundly specified in that they associate a unique outcome (allocation and transfers) to any valid input (bids). Having done so, we auto-generate verified executable…

Nearly fifteen years ago, Google unveiled the generalized second price (GSP) auction. By all theoretical accounts including their own [Varian 14], this was the wrong auction --- the Vickrey-Clarke-Groves (VCG) auction would have been the…

This paper studies inference in first-price and second-price sealed-bid auctions with many bidders, using an asymptotic framework where the number of bidders increases while the number of auctions remains fixed. Our approach enables…

We use formal methods to specify, design, and monitor continuous double auctions, which are widely used to match buyers and sellers at exchanges of foreign currencies, stocks, and commodities. We identify three natural properties of such…

Double auctions are widely used in financial markets, such as those for stocks, derivatives, currencies, and commodities, to match demand and supply. Once all buyers and sellers have placed their trade requests, the exchange determines how…

Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics…

This survey outlines a general and modular theory for proving approximation guarantees for equilibria of auctions in complex settings. This theory complements traditional economic techniques, which generally focus on exact and optimal…

We develop extensions to auction theory results that are useful in real life scenarios. 1. Since valuations are generally positive we first develop approximations using the log-normal distribution. This would be useful for many finance…

A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…

Real-time bidding (RTB) systems, which utilize auctions to allocate user impressions to competing advertisers, continue to enjoy success in digital advertising. Assessing the effectiveness of such advertising remains a challenge in research…

The standard framework of online bidding algorithm design assumes that the seller commits himself to faithfully implementing the rules of the adopted auction. However, the seller may attempt to cheat in execution to increase his revenue if…

Consider the problem of allocating goods to buyers through an auction. An auction is efficient if the resulting allocation maximizes total welfare, conditional on the information available. If buyers have private values, the…

In sponsored search, a number of advertising slots is available on a search results page, and have to be allocated among a set of advertisers competing to display an ad on the page. This gives rise to a bipartite matching market that is…

Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…

We provide efficient estimation methods for first- and second-price auctions under independent (asymmetric) private values and partial observability. Given a finite set of observations, each comprising the identity of the winner and the…

We show that in the single-parameter mechanism design environment, the only non-wasteful, symmetric, incentive compatible and Sybil-proof direct mechanism is a second price auction with symmetric tie-breaking. Thus, if there is private…

We propose a novel statistical learning method for multi-item auctions that incorporates credible intervals. Our approach employs nonparametric density estimation to estimate credible intervals for bidder types based on historical data. We…

Most of the work in the auction design literature assumes that bidders behave rationally based on the information available for every individual auction, and the revelation principle enables designers to restrict their efforts to incentive…