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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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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4 votes
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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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3 votes
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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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2 votes
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135 views

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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7 votes
1 answer
102 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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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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3 votes
1 answer
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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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2 answers
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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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3 votes
1 answer
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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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4 votes
3 answers
279 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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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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2 votes
2 answers
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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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2 votes
1 answer
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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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5 votes
4 answers
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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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5 votes
2 answers
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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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3 votes
1 answer
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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 ...
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6 votes
2 answers
93 views

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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2 votes
1 answer
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Allocating chores using auctions

I live in a student dorm with 16 people and we share a kitchen. Every week someone has to clean the kitchen. Right now we just take turns in a way determined by the numbers of our respective rooms. ...
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4 votes
1 answer
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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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1 vote
1 answer
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Uniform price vs discriminatory price double auction

Uniform price and discriminatory price double auctions are the most commonly used auction mechanisms in the trading markets especially in peer-to-peer energy trading markets. However, I could not find ...
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1 vote
1 answer
256 views

First-price symmetric auction with discrete value

I've been trying to work the following problem out but I can't quite seem to understand it, or the whole concept of first-place auctions. I don't understand how we get to the equilibrium. The problem ...
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2 answers
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What is equilibrium dependent upon in Generalized Second-Price Auctions?

Theory states that GSP auctions induce truthful bidding. Is it the case that this is true ONLY IF a) each of the bidders truthfully bids their value ($b_i = v_i$) (each bidder's optimal strategy) ...
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1 vote
1 answer
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How does your dominant strategy change in a second price auction if there are two items?

Suppose there are 4 individuals and two items in this particular(?) auction. I understand that the dominant strategy in second price auction is to bid your true value if there is a single item but I'm ...
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2 votes
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What is the privilege of a primary dealer?

Primary dealers have a privileged position, so there is value in being registered as a primary dealer. - https://economics.stackexchange.com/a/13450/8387 I was previously under the assumption that ...
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4 votes
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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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1 vote
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Hubzu.com bidding terminology - "value-based foreclosure auction" [closed]

The hubzu website often has properties for bidding that state "this is a value-based foreclosure auction, which means the beneficiary has provided a bid based on market value". However, it then ...
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1 vote
1 answer
208 views

Clearing price in a double auction market

I have been reading a paper on energy markets and I have stumbled upon double markets and clearing prices, which got me quite confused (bare in mind, I am relatively new to this topic). Quote from the ...
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2 votes
1 answer
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Monotonicity of second price auctions with bidder-specific reserve prices

I am having difficulty understanding the problem below: Given CDFs $F_1, ..., F_n$, prove that the allocation rule of a second-price auction with bidder-specific reserve prices is monotone. The item ...
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Is second price auction better than first price sealed bid auction? Why? [duplicate]

As I understand and have read the advantage of the 2nd price auction is that it encourages bidder to bid for 'true value', which I think can also be done with the 1st price sealed bid auction. I might ...
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3 votes
1 answer
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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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