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Getting Started
We seek a theory of bidding behavior in auctions.
Our theory will attempt to explain how peoples’ bids are related to their
individual valuations, or simply values, for the item being auctioned.
In mathematical terminology, we want a mapping from values to bids
.
A person’s value is the
hypothetical
price at which she is indiﬀerent
between buying the item and not buying it.
With this interpretation, the payoﬀ someone gets from winning an item in
an auction is the diﬀerence between her value and the
actual
price she
pays for it.
Rod Garratt
ECON 177: Auction Theory With Experiments
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View Full Document We cannot presume to know peoples’ values for items they bid on in
auctions.
An individual’s willingness to pay for something depends on.
...
•
how much satisfaction or enjoyment she gets from consuming it
instead of other things she could potentially consume in its place
•
their wealth or disposable income
These attributes are (typically) unobservable.
We can’t proceed unless we know something about individual values.
We assume that we know the range of possible values
that people hold
and the likelihood that someone’s value lies in any interval
.
Rod Garratt
ECON 177: Auction Theory With Experiments
Probability distribution function,
F
Let
v
i
denote individual
i
’s value
From the point of view of the auctioneer, or other bidders, or an economist
analyzing the auction, individual i’s value is a random variable ˜
v
i
The information the auctioneer has about the likelihood of diﬀerent
realizations of the random variable ˜
v
i
is summarized by the function
F
.
For any value v
,
the number F
(
v
)
tells us probability that an individual
has a value that is less than or equal to v
.
Rod Garratt
ECON 177: Auction Theory With Experiments
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You can think of the function
F
as representing the distribution of types of
people that exist in the population.
F
(
v
) is the fraction of the population with types less than
v
An individual shows up at an auction is a random draw from the population
Hence, the likelihood that she has a value in any range is simply given by
the fraction of the population that has values in that range.
Rod Garratt
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This note was uploaded on 12/26/2011 for the course ECON 177 taught by Professor Garratt during the Fall '09 term at UCSB.
 Fall '09
 GARRATT

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