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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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
472 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 with “buy-it-now” option

Consider the buy-it-now price often included in online auctions. Suppose that 2 bidders in an ascending oral (English) auction bid for an object. Each has values i.i.d uniformly on $[0,1]$. Suppose ...
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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
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
47 views

Deriving support in bidding strategy

I'm considering some question, and I'm not sure what it asks me to do: Consider a two-bidder auction with two types of players, high type and low type ($v_h>v_l$). The probability of a low ...
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1answer
75 views

How to prove that a point is a maximum point

I have the following function: $$ \Pi =\int_{0}^{z}[x_{1} + \alpha y + \alpha \frac{N-2}{2}y - \beta(z) - \gamma ( \beta(z) - \beta(y))](N-1)y^{N-2} dy $$ The first derivative with respect to $z$ is:...
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Not sure how to use this formula for auctions

In my textbook I was given this formula for auctions: As far as I understand, $N$ is number of people who place bets, $P_{personal}$ means my subjective value of the current lot (it's also assumed ...
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In US gov treasury auction, can the highest bidder force high prices for all others

In US treasury auction (for bonds and notes), my understanding is that the highest bidder's price (and rate) is applied for all the buyers. Assume a buyer 'A' who plans to buy a smaller number of ...
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2answers
154 views

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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1answer
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Incentive compatibility: Weakly dominant strategy versus Nash equilibrium?

When it comes to proving that a mechanism e.g. auction is incentive compatible this is the approach I'm using: I break down all the cases that might happen if the agent reports an untruthful value to ...
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1answer
255 views

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 ...
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Iterative versus continuous auctions

I'm a little confused about the terminology used in economics literature while describing iterative and continuous auctions. Have I understood the difference correctly? Iterative Auction: The ...
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1answer
254 views

Nash Equilibrium in 2 bidder auction

I am trying to find Nash Equilibrium of an auction with two bidders in which the highest bidder wins the object but both bidders pay the losing bid. Here every bidder follows the same bidding strategy ...
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2answers
61 views

How to decide the best bid in an auction?

I am going to participate in a decision committee of a governmental auction in energy market. I want to learn more about how to decide which bid is the best in short/mid/long term. Can you suggest ...
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126 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
611 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
343 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
339 views

What does speculative bid mean?

I tried to look for this term on the Internet, to no avail, as what I found does not fit into the context I found this word in. My context is: The incentive-compatible instrument of Vickrey Auction ...
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1answer
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What does it mean when we say an iso curve has no interior?

From the paper: "Standard Auctions with Financially Constrained Bidders" - by Che and Gale. The authors describe an isobid curve as the curve that represents payments of the same value in a 2-...
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1answer
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Auction and best response

Consider an auction in which $k$ identical objects are sold to $ n>k $ bidders. Each bidder $i$ needs only one object and has a valuation $v_{i}$ for the object. In the auction, simultaneously, ...
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2answers
929 views

One bidder in 2nd price auction

in second priced auctions, the highest bidder wins the auction and pays the price of the second highest bidder. What happens if there's only one bidder? That bidder would have won the auction, but ...
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1answer
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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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Does the VCG algorithm work for any bundle valuation function?

Assume we have $n$ buyers of $|M|=m$ items in a combinatorial auction. So as we know, we can use the Vickrey-Clarke-Groves (VCG) algorithm to allocate bundles of items to buyers as best as possible. ...
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Derivation of Equilibrium Strategy in 1st-price Auction?

Hey, everyone. I desperately need help understanding some math in auction theory. I have been writing a paper as an undergrad for auction theory, and after all of my research I just cannot understand ...
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331 views

Primary dealers in treasury auctions

When the treasury or equivalent institution of a country auctions of government bonds there is frequently (i.e. in most countries) some sort of restriction on who can participate. The term primary ...
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1answer
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Vickrey Auction question

I'm looking at this webpage here: https://gilkalai.wordpress.com/2013/05/18/test-your-intuition-21-auctions/ I've generated the R code below to simulate the value for each Bidder 1000's times. I'm ...
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Empirical Study of Auctions with Limited Data

I have limited real auction data which I am trying to see if I can do any empirical analysis. The data consists of auction type (i.e., forward or reverse), protocol (e.g., Vickrey, Dutch, English, etc....
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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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1answer
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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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2answers
312 views

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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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
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 ...
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1answer
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How do penny auctions make money? [closed]

What are penny auctions? Given the great discounts they claim (up to 95%), how do they make money?
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1answer
252 views

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
850 views

How to calculate expected revenue in reverse auctions (procurement)

I'm trying to find the correct formula to calculate de expected revenue of a reverse auction, properly, a second-price sealed-bid procurement auction to identify the lowest cost supplier. Prices are ...
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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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349 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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443 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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1answer
361 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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2answers
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
275 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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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
70 views

Is there an algorithm to find as many NE as possible in this generalized second price auction?

Suppose three advertisers, I, II, III are participating in an auction for three positions for online advertising, top, middle and bottom. Assume that click per second for a position is not affected ...
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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
266 views

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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3answers
125 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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4answers
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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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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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1answer
2k views

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 ...