10
votes
Accepted
What is virtual valuation?
Suppose you face a single buyer whose willingness to pay, $v$, is distributed according to $F(v)$. If you charge a price $p$, he will buy if and only if $v>p$, leaving you with expected revenue of $...
- 16.7k
9
votes
Impact of auction systems that allow 'sniping'
Firstly, it's right to say that the hard ending rule on ebay seems to be behind sniping. Here's a figure from Roth & Ockenfels' AER paper:
On eBay (fixed end time) bids arrive much later than on ...
- 16.7k
9
votes
Accepted
How to auction shared item with a roommate?
If you think that the distribution of your value and your roommate's value are the same then I would suggest that you consider the following bidding protocol:
each bidder submits a sealed bid, $b_i$.
...
- 16.7k
9
votes
Accepted
What is the point of silent auctions?
But perhaps this is not always the case. The price might have been so high that you would not have been willing to bid above it. In fact it might have been so high that the no one but the highest ...
- 27.7k
8
votes
Accepted
Are spectrum auctions a tax?
Suppose you write some software that you can then freely sell at practically no cost per unit (the wonders of the internet). You want to make as much profit as possible. Since you have almost no per ...
- 10.5k
7
votes
Accepted
Auction models for tickets
First, you should note that there is a Revenue Equivalence Theorem that says under a set of conditions, the seller's revenue from using different forms of auctions will be the same. This same result ...
- 15.1k
7
votes
Accepted
How are ties broken in a second price sealed bid auction?
The winner pays the second highest bid, which is 5 dollars, however who the winner is depends on the tie-breaking rule. There are multiple rules one could use. In most cases it is assumed that the ...
- 27.7k
7
votes
Accepted
Differential equation for first-price auction
For notational simplicity, let me define the distribution $G(s) = F^{N-1}(s)$ with density $g(s)$. Let $\underline{s} = 0$ (for simplicity).
We have
$$
b'(s)G(s)+b(s)g(s)=s g(s)
$$
Integrating to $x$ ...
- 1,829
6
votes
Accepted
Optimal Random Bids
First I will just show that the 0.5 (or $\frac{1}{2}$) cut-off point does not work as a symmetric equilibrium, then you can decide for yourself if you want to think about the problem or read the ...
- 27.7k
6
votes
Accepted
Are lotteries auctions?
Generally, and surprisingly, yes, lotteries are similar to auctions. What do I mean by that?
In an auction, you increase the likelihood of winning by increasing your bid. In many auctions, if you ...
- 10.6k
6
votes
Accepted
How do penny auctions make money?
In a penny auction, each bid raises the going price of an object by just one penny. However, placing such a bid is costly whether or not you win. Usually it costs one dollar to place a bid -- ...
- 825
6
votes
What are the benefits of a first price sealed bid auction?
If there is a single item for sale, bidders are risk neutral, and bidders have independently and identically distributed private values then any two auctions that
allocates the item to the highest ...
- 16.7k
6
votes
What are the benefits of a first price sealed bid auction?
A good article to read about this is by Susan Athey, Jonathan Levin and Enrique Seira. It has the title: "Comparing Open and Sealed Bid Auctions: Theory and Evidence from Timber Auctions," was ...
- 551
6
votes
Accepted
2 Player All-Pay Auction
This seems like a basic issue about probability calculus/theory.
The intuition behind the uniform distribution over $[a,b]$ is that all outcomes between and $a$ and $b$ are equally likely. Because of ...
- 27.7k
6
votes
Accepted
Bayesian-Nash equilibrium in a first-price auction
It is actually assumed that $b_i(v_i)$ is of the form $\alpha_i+\beta_i \cdot v_i$. So it is an affine function. Linearity only works if the bottom of the uniform distribution is 0.
A somewhat ...
- 27.7k
6
votes
Accepted
In auction theory, why is my own valuation a random variable?
In most of the literature I have read on private value auctions you do actually know your own valuation in the auction, it is your private information. It has a distribution from the point of view of ...
- 27.7k
6
votes
Auctions and finding nash equilibrium of a dynamic game
You are only required to get Nash equilibria and not sequentially rational/subgame perfect equilibria. Hence Player 2's actions at information sets that do not occur (that do not reflect Player 1's ...
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6
votes
Auctions and finding nash equilibrium of a dynamic game
Let's first determine the sets of actions of the players.
An action of player 1 is simply a bid $x_1 \in \mathbb{R}_+$.
An action of player 2 is a function: $f_2: \mathbb{R}_+ \to \mathbb{R}_+$ that ...
- 8,662
5
votes
Impact of auction systems that allow 'sniping'
If bidder valuations are dependent on the information revealed by other bids (particularly increasing in their number and level), then we would expect too low bids because bidders have to internalize ...
- 16.1k
5
votes
Reverse auction formula
A first price standard and reverse auction are formally equivalent to each other, and the same method can be used to solve both:
First Price Auction
In a first price auction, $n$ bidders choose ...
- 16.7k
5
votes
Bidder Count Impact on Uniform Price Economics
It is a known result in Mechanism Design that both first-price as well as second-price auctions yield the same expected revenue, under certain conditions (like independence of valuations, private ...
- 32.7k
5
votes
What are the advantages and disadvantages of second price auctions?
A lot of questions here. Might be helpful to split them into different posts, but let's take a crack at them.
The reason why the second price sealed auction is set up this way is simple. Imagine you ...
- 6,476
5
votes
Reverse Auction bidding strategy
Given the very general description of the problem, I can think of the following (also very general) way of formulating it mathematically.
Let $v_n$ be the buyer's value from owning $n$ plots of land,...
- 15.1k
5
votes
Accepted
Ex-post vs Ex-ante Budget Balance in Auctions
These are widely used technical terms with a precise mathematical meaning:
Ex-ante budget balance means that the expected sum of all transfers is zero.
Ex-post budget balance means that the sum of ...
- 10.5k
5
votes
Accepted
Virtual valuation when the distribution is discrete
Virtual valuation is the derivative of the expected revenue function with respect to the tail probability $q$ that is then evaluated at value $v$. The Revenue function is
$$R(q) = q\cdot v(q),\;\;\; q ...
- 32.7k
5
votes
Why are second price auctions preferred if they don't maximize expected revenue?
I don't think sellers would prefer SPA over FPA. In fact, the SPA is riskier than the FPA, if we look at it from a seller's perspective. The reason is because the distribution of prices in case of the ...
- 515
5
votes
What is virtual valuation?
The idea is simple: the seller wants to target that individuals who's ready to pay him the highest amount, thus targets the person with the highest virtual valuation.
To target the individual who's ...
- 515
5
votes
Accepted
Auction with one buyer and multiple sellers
Such a setting is called a "procurement auction" or "reverse auction."
It does not fundamentally change anything. Instead of buyers with privately known valuations, the auctioneer ...
- 5,120
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