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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15 views

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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1answer
129 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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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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304 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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74 views

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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1answer
55 views

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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1answer
112 views

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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2answers
487 views

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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82 views

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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80 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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50 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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1answer
674 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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1answer
84 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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29 views

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
103 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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1answer
104 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
51 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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34 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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3answers
210 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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38 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
41 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
31 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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1answer
52 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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1answer
35 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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2answers
78 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
72 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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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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1answer
47 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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1answer
140 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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1answer
31 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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72 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
93 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
130 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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54 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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27 views

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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59 views

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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279 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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1answer
155 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
99 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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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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33 views

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
284 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
77 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
158 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
210 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
120 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
206 views

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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4answers
2k views

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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816 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 ...