Questions tagged [auctions]

Procedures in which participants submit bids, with resources being allocated among bidders in accordance with some pre-specified rule.

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3answers
705 views

Impact of auction systems that allow 'sniping'

I'm a bit perplexed that eBay has auctions that have a fixed time ending, and so winners are often determined by who can 'snipe' the auction, by putting in the winning bid at the last possible ...
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1answer
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eBay economics - total revenue impact from expanding ecosystem by 1 seller

While I think my question is straight forward, I'm guessing the answer to it is anything but. Thanks in advance for any insight you may be able to offer, even if it's just a directional assist. Here'...
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What are the benefits of a first price sealed bid auction?

All parties make a single bid. But do not disclose the bid to peers. The organizer chooses the maximum (or minimum) bid as the winner. What are benefits of such a system as opposed to normal auction ...
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How to auction shared item with a roommate?

My roommate and I split the cost of a game console a year ago (~$400) but he is now moving out. We were wondering how to fairly auction the console given the situation: We both paid an equal price ...
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2answers
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What is virtual valuation?

I’m reading through a textbook in auction design when it describes a term, virtual valuation $$\phi_i(v_i) = v_i - \frac{1 - F(v_i)}{f(v_i)}$$ where $f$ is the pdf of a bidders valuation and $F$ is ...
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439 views

Optimal Random Bids

This question comes from this website that I peruse often. Two players go on a hot new game show called “Higher Number Wins.” The two go into separate booths, and each presses a button, and a ...
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1answer
75 views

Differential equation for first-price auction

I want to solve a differential equation of the first-price auction. In particular, from Jonathan Levin's October 2004 lecture notes, we have the following differential equation: $$b'(s) = (s-b(s))(n-1)...
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445 views

Are lotteries auctions?

I heard one professor of my university say that "lottery is a kind of auction. So we can predict it! Then we could get a lot of money!" Since he is in the mathematics department, and I know little ...
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140 views

Can't Derive Expectation in Second Price Auction

I'm working on a SPA where we solve: $\max_{\beta \ge 0} Pr\{Winning\}[v - \mathbb{E}(b^{[2]} \ | \ b^{[2]} \le \beta)]$ We assume all beliefs on bids are independently and identically distributed ...
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1answer
305 views

What is the point of silent auctions?

A while back, someone decided to auction off something unique and valuable, as a silent auction: everyone would submit one bid only, and whoever bid the highest would win. I submitted a bid that I ...
6
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1answer
487 views

Bayes-Nash equilibrium in Auction

Consider a seller offering a single object for sale to two buyers with independent valuations – each bidder’s value is uniformly distributed on [0,1]. Assume that buyer 1 submits a bid that buyer ...
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1answer
127 views

Auction models for tickets

Consider a typical event for which tickets are sold. The event only occurs once, and for simplicity we can assume that only one kind of ticket is provided, i.e, no VIP seats etc. $N$ tickets are ...
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1answer
474 views

Bayesian-Nash equilibrium in a first-price auction

In a famous textbook example of a Bayesian-Nash equilibrium, there is a first-price auction with two independent players. Each player $i$ values the item as $v_i$, which is distributed uniformly in $[...
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Auction theory reference request

I am interested in finding the literature or at least some references (books, journal papers etc.) for the following problem: Suppose there is an auction with one seller and one buyer. The seller ...
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2answers
1k views

In auction theory, why is my own valuation a random variable?

Auction theory typically (always?) begins by assuming that each bidder's valuation is a random variable. Now, it might seem reasonable (at least from a Bayesian perspective) for you to treat other ...
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1answer
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What types of 'market mechanisms' are said to exist besides auctions?

The book Understanding Auctions states: The term auction covers a wide range of market mechanisms that are used to exchange products and services by determining who receives an item and how much is ...
6
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1answer
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Arguing uniqueness of Bayes-Nash equilibrium in an auction setting

In an auction setting with interdependent values, let $\theta_i$ denote the type of player $i$ and $m_i$ that player's message (a bid, essentially). I have calculated the best response function as: $$...
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1answer
362 views

System of Differential Equations- Asymmetric First-Price Auction

I am working on a problem in my Auction Theory textbook regarding a two-player asymmetric first price auction. Assume the bidders are risk neutral. The problem statement is as follows: Suppose ...
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3answers
276 views

Multi-item Auctions in Mechanism Design

I'm new to auction theory and only started reading it a few days ago. My question is this: Is it possible to design efficient auctions of multiple non-identical items? By efficient I mean maximize the ...
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1answer
1k views

How are ties broken in a second price sealed bid auction?

Say there are two people who evaluate an object at 5 dollars and a third who evaluates it at 4 dollars playing a second price sealed bid auction. The first two bid 5 dollars and the third bids 4 ...
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1answer
615 views

Reverse Auction bidding strategy

A buyer wants to buy contiguous land plots from three landowners (sellers) who own fixed size plots. Sellers have their private valuation of their plots. The buyer will hold a closed bid procurement ...
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1answer
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What are the advantages and disadvantages of second price auctions?

I am reading https://en.wikipedia.org/wiki/Vickrey_auction about second price auctions. It seems counterintuitive to me that the winning bidder pays the bidding price of the runner-up bidder, rather ...
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Approximately Optimal Mechanism Design vs. Revelation Principle

The abstract of the article "Impossibility Results for Truthful Combinatorial Auctions with Submodular Valuations" (Dobzinski, Vondrak, 2016) states A long-standing open question in algorithmic ...
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1answer
251 views

Fantasy football

I have an idea for a fantasy football experiment looking at three different areas of the draft. These three areas are the position of each pick and how often and what value are trades. I have dug ...
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2answers
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Bayesian Mechanism vs Prior-free Mechanism

I have a double auction mechanism in which the valuations of the agents for the items are drawn from a known random distribution. To be precise, the valuations are the probability of each agent ...
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2answers
350 views

Two-player first-price auction with resale

Exercise 2.5 in Vijay Krishna's Auction Theory (slightly modified): Consider a two-bidder first-price auction in which bidders’ values are distributed according to $F$. Let $\beta$ be the ...
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How to find an optimal strategy in an auction?

I have asked this question in mathematics forum as well but since I have not recieved an appropriate answer yet, I ask it here as well. Consider an auction of sculptures by four artists: A, B, C and D....
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Auction mechanism with no trusted third-party

I have been using a double-auction mechanism to solve a two-sided market where multiple agents are competing to supply/use slices of a shared resource. The owner of the resource is a trustable third-...
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Can repeated bidding in an auction make each player's type common knowledge?

In Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007), there's a hand-waving argument to justify their setting as a game of complete information: we assume that all values are common ...
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1answer
659 views

Are spectrum auctions a tax?

According to Wikipedia, A spectrum auction is a process whereby a government uses an auction system to sell the rights to transmit signals over specific bands of the electromagnetic spectrum and to ...
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164 views

Auction with one buyer and multiple sellers

In the standard auction model, there are one seller and multiple buyers, the bidders are the buyers. Consider now an auction with one buyer and multiple sellers, where the bidders are the sellers. ...
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1answer
438 views

Ex-post vs Ex-ante Budget Balance in Auctions

Have I understood this correctly? When I say my auction mechanism is ex-post budget balanced it means that in practice (I have done market simulations) and according to the results my mechanism is ...
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1answer
202 views

Auctions with affiliation

This problem is an example given in Vijay Krishna's Auction Theory (2nd Edition, Chapter-6, Example 6.2). The problem is as follows: Suppose $S_1,S_2$, and $T $ are uniformly and independently ...
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1answer
277 views

“Auction” versus “Bidding war”

Real estate sales sometimes occur at an official auction. But sometimes a seller who does not take their house to auction may find themselves entertaining multiple bids for the house. In this case, ...
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1answer
110 views

Are there multiple equilibria in the second price auction?

Suppose that $n\geq 2$ bidders compete in a second price auction. Each bidder $i$ knows their own valuation $v_i$, but only knows the distribution generating the valuations of the other players. ...
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1answer
3k views

Difference between double auction and continuous double auction?

What is the difference between double auction and continuous double auction? Sometimes I feel that they were types of two-sided auction but sometimes I feel as if they were two separate concepts.
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2answers
1k views

First-price auction with discrete values

Exercise 4.5 in Vijay Krishna's Auction Theory: Suppose that bidder 1 always has value $X_1=2$, while bidder 2's value, $X_2$ is equally likely to be $0$ or $2$. Find equilibrium bidding strategies ...
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1answer
34 views

Incentive compatibilty conditions for multi-item auctions

In this paper by Myerson on optimal single item auctions, the incentive compatibility condition is shown to be equivalent to the following simpler conditions on the auction - (i) the allocation ...
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0answers
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Unique Nash-equilibria in multi-unit auctions with uncertain participation

Setup Consider a one shot sealed bid multi-unit auction where $N$ bidders compete for $K$ identical objects and each bidder $i$ has demand $d_i\in \{1,\dots,K\}$. Bidders receive private i.i.d. ...
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4answers
765 views

Why are second price auctions preferred if they don't maximize expected revenue?

The reasoning usually given for why you would use a second price auction (SPA) as opposed to a first price auction (FPA) is that FPA encourage underbidding while SPA encourage truthful bidding. That ...
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3answers
126 views

Bidder Count Impact on Uniform Price Economics

Say we have an uniform price auction where 1 really rare stamp is for sale. Only 5 randomly selected stamp collectors are invited to bid and the stamp ends up selling for 1 million dollars. Now ...
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1answer
344 views

2 Player All-Pay Auction

Consider a 2 player all-pay auction, bidding for $1. Each submits a bid that is a real number, thus $S_i=[0,\infty)$. The player with a higher bid wins $1, but both players must pay the submitted bid....
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1answer
100 views

Is VCG mechanism applicable in reverse auction? If so, how?

The VCG mechanism I've learnt is from Roughgarden's Twenty Lectures on Algorithmic Game Theory. Given an auction, we first identify the allocation that maximize the social welfare and then compute the ...
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1answer
43 views

What's the definition of social welfare in a procurement auction?

In single item forward-auctions, the social welfare is defined as: $$\sum_{i=1}^{n} v_i x_i$$ where $v_i$ is buyer $i$'s valuation for the item, and $x_i$ is a binary variable indicating whether or ...
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1answer
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Reverse auction formula

I am studing a little bit of auction theory. I found the optimal bid value in the Milgrom paper for the first price auction that is $$ P=v \frac{n-1}{n} $$ where $P$ is the optimal bid, $v$ is the ...
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1answer
67 views

Expected payment in a second price auction with affiliation

The symmetric bidding strategy in a second-price auction with affiliation is given by $\beta(x)=v(x,x)$, where $v(x,y)=E[V_1|X_1=x,Y_1=y]$ (here $Y_1$ is the highest ordered statistic among the ...
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2answers
211 views

Virtual valuation when the distribution is discrete

The virtual valuation of a buyer in an auctin is a function used to calculate the expeced revenue of a seller from that buyer. When the buyer's value comes from a continuous distribution with pdf $f$ ...
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1answer
172 views

The Price is Right Bidding Strategies

I am currently reading this article. If you are unfamiliar with the game, "The Price is Right", at the beginning, four bidders are selected who have to guess the price of some consumer object. ...
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1answer
261 views

Marginal Revenue Interpretation of Auctions

I'm reading Klemperer's survey on auction theory (pages 17-18) which discusses the relation between traditional microeconomic price theory and the revenue equivalence result. Firstly, I don't quite ...
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1answer
57 views

Uniqueness of equilibria in first-price auction with discrete valuations

Assume we have a first-price auction with discrete and independent private values and identical distributions of all bidders. It is known that there exists a Bayes-Nash equilibrium where bidders bid ...