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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33 views

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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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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73 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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23 views

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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1answer
99 views

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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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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52 views

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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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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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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35 views

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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2answers
36 views

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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1answer
48 views

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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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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117 views

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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30 views

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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45 views

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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66 views

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
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 ...
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65 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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1answer
81 views

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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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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1answer
23 views

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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92 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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53 views

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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1answer
29 views

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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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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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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222 views

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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121 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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1answer
98 views

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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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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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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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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Is there a way to eliminate shilling, spiting, and overbidding in second price auctions?

In a 2nd price option, if all the player choice their bids independently, the optimal strategy is to bid their valuation. However, in some situations, their decisions can effect each other. For ...
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1answer
108 views

Best-responding to a stochastically higher distribution of bids

In Auction Theory, Krishna writes that: a bidder who faces a stochastically higher distribution of bids–in the sense of reverse hazard rate dominance–will bid higher (This follows the proof of ...
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58 views

Buyer's efficiency in auctions

first and foremost, I'm not an economist, probably a scientist though. In my country the most popular way to buy and appartment or a house is by first-price-auctions (the highest bid takes it all). ...
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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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Ausubel (2004) auction, any implementation?

I'm looking for an implementation of the ascending-bid auction introduced in his 2004 AER paper. More specifically, a market using this framework which either has been reviewed by other scholars or ...
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1answer
817 views

All-Pay Auction Mixed Strategy Equilibrium

I am currently struggling with this exercise. Professor Nash announces that he will auction off a 20 dollars bill in a competition between two students chosen at random. Each student is to privately ...
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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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1answer
1k views

First Price Auction with Reserve Price

I'm trying to solve the following question: "The seller wants to auction off a single item to two bidders, the valuation of each bidder is an iid draw from a uniform distribution on $[0,1]$ where ...
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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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Charging a minimum increment on the second price in online advertising auctions

Many ad servers running GSP auctions tend to charge a $0.01 increment on the second price. I was wondering if there was any theoretical basis for this, or is it just a way for ad servers to make a ...
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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
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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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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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2answers
210 views

Second Price Auction - adjusting PDF for reservation price

The situation: There is a second price auction with 2 players. Consider a second-price auction with 2 players. Their valuations of the object at auction are and are independently and identically ...
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159 views

Auction question

I’m studying on auction. But I couldn’t understand some questions about this topic. And I cannot solve such type questions. For example, I know that a set of symmetric and risk neutral bidders ...