# 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 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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### 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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### 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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### 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 find ...
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### How to calculate clearing when supply demand curve do not intersect

I am working on a P2P energy trading project and want to implement a uniform price double auction. I have confusion about how the clearing price will be determined if the supply-demand curves do not ...
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### 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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### 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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### 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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### Regarding exchanges (crypto exchanges or equity exchanges) is there a reason Vickery auctions (second price sealed bid auctions) are not used?

Is there any benefit to the current choice of auctions in exchanges or conversely any reason why no one has used Vickery auctions in equity exchanges. I know they're used in ad auctions.
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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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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### 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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### 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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### 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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Many ad servers running GSP auctions tend to charge a $0.01 increment on the second price. I was wondering if there was any theoretical basis for this, or is it just a way for ad servers to make a ... 2answers 150 views ### Virtual valuation when the distribution is discrete The virtual valuation of a buyer in an auctin is a function used to calculate the expeced revenue of a seller from that buyer. When the buyer's value comes from a continuous distribution with pdf$f$... 1answer 661 views ### How are ties broken in a second price sealed bid auction? Say there are two people who evaluate an object at 5 dollars and a third who evaluates it at 4 dollars playing a second price sealed bid auction. The first two bid 5 dollars and the third bids 4 ... 1answer 291 views ### Ex-post vs Ex-ante Budget Balance in Auctions Have I understood this correctly? When I say my auction mechanism is ex-post budget balanced it means that in practice (I have done market simulations) and according to the results my mechanism is ... 2answers 192 views ### Second Price Auction - adjusting PDF for reservation price The situation: There is a second price auction with 2 players. Consider a second-price auction with 2 players. Their valuations of the object at auction are and are independently and identically ... 1answer 113 views ### Auction question I’m studying on auction. But I couldn’t understand some questions about this topic. And I cannot solve such type questions. For example, I know that a set of symmetric and risk neutral bidders ... 2answers 1k views ### In auction theory, why is my own valuation a random variable? Auction theory typically (always?) begins by assuming that each bidder's valuation is a random variable. Now, it might seem reasonable (at least from a Bayesian perspective) for you to treat other ... 1answer 402 views ### Bayesian-Nash equilibrium in a first-price auction In a famous textbook example of a Bayesian-Nash equilibrium, there is a first-price auction with two independent players. Each player$i$values the item as$v_i$, which is distributed uniformly in$[...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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....