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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Auction with independent private values - An example from Game Theory: Analysis of Conflict by Roger Myerson
I have difficulties understanding the equilibrium analysis of the following auction game:
Suppose that there are $n$ bidders in an auction for a single indivisible object. Each player knows privately ...
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Define "Equilibrium" in Market Design task
in a current market design problem set I am very confused by the given questions.
We are often asked to find "an equilibirum of the [auction type, e.g. second-price auction]".
The amount of ...
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Equilibrium of Perturbed Dollar Auction Game - An Example from Game Theory: Analysis of Conflict by Roger Myerson
I am studying game theory using Myerson's textbook (Chapter 3 - Equilibria of Strategic-Form Games, Section 3.6 - The Decision-Analytic Approach to Games). I have difficulties understanding and ...
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Why do all filled bids receive the same rate, which is the rate of the lowest filled bid, during the US Treasury auction process?
This question pertains to the US Treasury auction process. {1} states:
Treasury auctions are designed to minimize the cost of financing the national debt by promoting broad, competitive bidding and ...
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The mathematical denotion of why each bidder bids the expected 2nd highest bidder's value in first-price auctions
Advanced Microeconomics by Jehle and Reny (p431) contains the following theorem:
And also these comments:
Because FN-1(·) is the distribution function of the highest value
among a bidder’s N - 1 ...
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Third price auction from Auction Theory by Krishna, Order statistics
Notation:
$Y_1$: Highest order statistics of $(N-1)$ players' valuation.
$F_n^M:$ The distribution function of the highest $n$th order statistics of $M$ players.
$f_n^M:$ The density of the highest $n$...
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Geometric interpretation of transfer function in incentive-compatible direct mechanism
Consider a set of players $i = 1,...,N$ who need to allocate some good. Each player $i$ valuates the good $v_i \in [0,1]$, with $v_i \sim f_i$. An individually rational direct mechanism $(p,c)$, with $...
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How widely can the objective of mechanism design be generalized?
The mechanism design lectures I've been watching have focused on the objective of maintaining performance guarantees in terms of either total surplus or total revenue/virtual surplus (while also ...
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Interpretation of the Myerson (1981) Bidder Utility (Optimal Auctions, Mechanism Design)
In Myerson 1981, the bidders' utility function does not make sense. $p_{i}$ is a probability of winning the auction, $t_i$ is the bidder's type (or valuation of the item), and $x_i$ is the payment. $r$...
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Understanding How to Counter the Winner's Curse
In both popular level books on economics/rationality/etc., and videos of actual economics lectures, I keep running into the suggestion to bid in a common value auction as though victory is already ...
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Expected revenue maximizing auction & ex-post efficiency
Is it true that in the design of the expected revenue maximizing auction in the standard independent private value setting, the allocation of the object may be ex-post inefficient?
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Is there any known algorithm to negotiate a price between co-owners who want to sell an item? [closed]
I am looking for an algorithm or a mechanism that I could implement for a specific case in my smart contract. How can multiple co-owners of an item agree efficiently on a selling price?
I am not ...
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How the fed influences treasury rates through open market operations
Lower yields through open market operations
When the fed wants to put downward pressure on treasury rates, one tool it can use is open market purchases of the tenor it wants to push yields down on. ...
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All-pay auction question
Two players take part in the following auction for a £1000 prize. The two players submit bids simultaneously, and the higher bid wins the prize (if bids are identical each gets £500). Both the winner ...
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How does the punchline in this SMBC comic about "Vickrey-Clarke-Groves auctions" work?
Saturday Morning Breakfast Cereal (SMBC) showed this comic today:
I'm not entirely sure I understand this punchline. Based on what Wikipedia tells me about this form of auction, it appears to be a ...
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Public/private knowledge in auctions
Consider three firms that engage in a first-price auction. Firm $i$'s payoff when firm $j$ wins the auction is $S_{i,j}$, which is deterministic and publicly known.
The winning firm $i$ has to pay ...
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Single-item single-bidder: why posted price is the only possible DSIC mechanism?
I'm reading Tim Roughgarden's Twenty Lectures on Algorithmic Game Theory. Lecture 5 is on revenue-maximizing auctions. It claims that in the single-parameter qusilinear environment, for the extremely ...
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Price achievable in sealed-bid pay-as-bid energy auctions
Situation
I am modeling an auction-based electricity market. Lets assume they call an auction for 500MWh, and participants can submit bids of at least 1MWh for a given price of $x$ EUR/MWh. Each ...
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Revenue-maximizing auction with no free disposal
Myerson has a famous theory that can be used to design truthful auctions maximizing the revenue of the seller. The simplest case is when a seller sells a single item to buyers whose values are ...
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A Gamma-Weibull distribution for empirical auction model
I am reading Comparing Open and Sealed Bid Auctions: Evidence From Timber Auctions (working paper version) and struggling with getting a log likelihood function about a Gamma-Weibull distribution. In ...
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First-order condition with arbitrary function
I am trying to use an auction model to simulate bids in a uniform price carbon emissions auction. That means it would be an auction with multiple bidders and one seller selling multiple units, or ...
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What is the expected payoff for a bidder in a second-price auction with N uniform distributed bidders, when the auctioneer sets a reserve price?
I would like to know what bidder i's expected payoff looks like in a second-price auction with $N=\{1,2,...,n\}$ bidders, where each bidder $i\in N$ has independent and uniform distributed valuations $...
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Is it a weakly dominant strategy to bid your true value in a third-price auction with two identical goods and N uniform distributed bidders?
I am interest in finding the optimal strategy for a single bidder (the BNE), when I have a third-price auction with N bidders and two identical goods. The bidders have iid valuations: U(0,1)
I have ...
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Mechanism design making the Government reveil its indiferrence price towards goods
In order to Tax non-monetary property and wealth the government sets an arbitrary price (they are not even personalized assesments) and often people transact below that price. I have bought and sold ...
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Are there any economic reasons why luxury goods should not be auctioned off, or at least dynamically priced, when facing shortages?
Over the last year many prominent examples come to mind, where there does not seem to be any limiting moral or ethical reasons, and are simply not available most of the time due to demand greatly ...
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Auction mechanism with quoters and price takers
Consider a market with one buyer with a fixed demand and multiple sellers for a divisible good. The goal of the market is to determine a uniform unit-price for the good as well as which seller ...
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What would be the Dual Expected Utility function for an English Auction?
So the DEU function is $$V(p)= \Sigma \,x_i\pi_i(p),$$ and since an auction only has two outcomes for a bidder, failure (with probability $p$) or success (probability $1-p$) the function becomes $$V(p)...
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Two Sellers, One Buyer Auction
Consider the following game. There are two sellers, each of whom can produce one unit of
an indivisible good. The cost of producing the unit for seller i is $c_i$
. There is a single buyer
who wishes ...
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Auctions and finding nash equilibrium of a dynamic game
Suppose we have a sequential version of an Auction game:
• Player 1 places a bid.
• Player 2 observes player 1’s bid, then places a bid.
• The player with the highest bid wins the item at auction.
• ...
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Uniform price vs. pay-as-bid auctions in energy markets
These two types of auctions are most commonly used in the energy trading markets. What would be advantages and disadvantages of each? And in the end, can we expect them to deliver similar outcome?
One,...
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Auction Theory: Proving that the found equilibrium is indeed optimal
I have been looking at auction theory and in the book Auction Theory by Krishna, there is one (seemingly simple) inequality that I just cannot follow.
Context: given a private valuation $x$, the ...
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Multi dimensional Auction in economics
I am following this paper . They have different suppliers and one buyer and They are using auction to select best suppliers Suppliers will submit. suppliers offer a multidimensional bidding on quality ...
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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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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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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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Economics behind reverse auctions with occasional non-profiting suppliers
I was curious about the theory behind a reverse auction system where some suppliers act in a non-profit manner, namely, that their consideration of extra-auctions benefits of providing their service ...
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Market clearing price and dual variables in auctions
Suppose the allocation of an auction (or a market) is defined by the solution of a linear program.
Then it is known that the associated clearing price is given by the dual variable associated to the ...
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The influence of restricted type space on incentive compatible mechanism design?
When we are to design an IC mechanism for an auction, we usually assume that each agent $i$'s type $\theta_i$ is draw from its type space $\Theta_i$, which contains all the possible types of $i$. For ...
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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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Whats the name of the famous hostile takeover where the winner payed less than the loser
In my studies I learned about a bid war ending in a hostile takeover where the winner ended up paying less than the loser offered. It is a very nice demonstration of elements of game theory so I would ...
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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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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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Deciding the winner in a Product-Mix auction
I am trying to understand how does Klemperer's Product-Mix auction work.
As I understand, given a supply I want to sell and a group of bidders, an auction system should determine who receives the ...
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Multi-item multi-unit matching markets
This is a reference request.
I'm interested in auction design problems of the following form:
- Consider one seller and many buyers.
- The seller seeks to sell multiple items where each item has ...
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What is 2nd round of rationalizability for a 1st price auction?
Consider a first-price auction.
Suppose that we have $N$ bidders, and they believe that their opponents' values is drawn from a uniform distribution on interval $[0,1]$.
Let us eliminate weakly ...
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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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First Price Auction (Expected Payoff)
I'm trying to solve followed first-price auction problem.
Bidder's pdf is
$$
f(v_i)= \begin{cases}
\dfrac{1}{8}v_i, & \text{if} & 0\leq v_i\leq4\\
0, & \text{if} & \text{otherwise}\\
...
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Efficiency in Auctions
Consider a finite number of bidders, each bidding for a single indivisible object, with private independent values from some probability distribution.
There are 2 intuitive notions of (ex-post) ...
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Reduction Rules for Auction conflicting Deals
This question addresses an interdisciplinary science between Computer Science and Economics (Modern Auction Design).
I'm posting my question here to get ur expert opinion as economists on the ...
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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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