Publication

Regret Minimization and Separation in Multi-Bidder Multi-Item Auctions

Abstract

We study a robust auction design problem with a minimax regret objective, where a seller seeks a mechanism for selling multiple items to multiple anonymous bidders with additive values. The seller knows that the bidders' values range over a box uncertainty set but has no information about their probability distribution. This auction design problem can be viewed as a zero-sum game between the seller, who chooses a mechanism, and a fictitious adversary or `nature,' who chooses the bidders' values from within the uncertainty set with the aim to maximize the seller's regret. We characterize the Nash equilibrium of this game analytically. The Nash strategy of the seller is a mechanism that sells each item via a separate auction akin to a second price auction with a random reserve price. The Nash strategy of nature is mixed and constitutes a probability distribution on the uncertainty set under which each bidder's values for the items are comonotonic.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related concepts (35)
Auction
An auction is usually a process of buying and selling goods or services by offering them up for bids, taking bids, and then selling the item to the highest bidder or buying the item from the lowest bidder. Some exceptions to this definition exist and are described in the section about different types. The branch of economic theory dealing with auction types and participants' behavior in auctions is called auction theory. The open ascending price auction is arguably the most common form of auction and has been used throughout history.
Nash equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.
Probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.
Show more
Related publications (38)

Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

Paolo Pegolo

We propose a novel approach to evaluating the ionic Seebeck coefficient in electrolytes from relatively short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and Bayesian regression analysis. By exploiting the ...
Amer Chemical Soc2024

New Perspectives on Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization

Daniel Kuhn, Florian Dörfler, Soroosh Shafieezadeh Abadeh

We study optimal transport-based distributionally robust optimization problems where a fictitious adversary, often envisioned as nature, can choose the distribution of the uncertain problem parameters by reshaping a prescribed reference distribution at a f ...
2023

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Daniel Kuhn, Zhi Chen, Wolfram Wiesemann

Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affec ...
2022
Show more