Econ 177
Sample Questions Part II
1. Consider a second-price auction with a single private value bidder who
value is drawn from the uniform distribution on [0,100]. You are the
seller.
(a) Compute the optimal reserve price assuming your value for the
item
Introduction to Auction Theory
Econ 177
Spring 2011
Introduction: A Historical Perspective
Herodotus reports that auction were used in Babylon as early as 500
B.C.
193 A.D. the Pretorian Guard sold the Roman Empire by means of
an auction
Wide array of com
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 mappin
Bidding Behavior
We assume people attempt to maximize their payo from participating in
an auction.
Hence, we are in a sense trying to determine their optimal bids.
However, an auction is a game in which the payo an individual earns
from any given bid depe
Expected Revenue
Here we calculate the expected revenue under the ecient equilibrium
bidding strategies for the rst- and second-price auction formats.
In a rst-price auction with F () uniform on [0,100], the symmetric
equilibrium bidding strategy has each
Professor Rod Garratt
ECON 177
Midterm
April 27, 2011
The exam is worth a total of 30 points. You have 1 hour and 15 minutes to complete this
exam. Good Luck!
In all the questions that follow you may assume each of the i=1,.,n bidders' values are
drawn in
Discrete Bids
Average Bid if saw 0: 1.364
Average Bid if saw 3: 2.73
Average Profit = .462 million
Number positive = 6, Number negative = 4, Number zero = 3
Continuous Bids
Average Bid if saw 0: 1.316
Average Bid if saw 3: 2.605
Average Profit = .649 mill
Econ 177
Sample Questions Part I
In all the questions that follow you may assume each of the i = 1, ., n
bidders values are drawn independently from the uniform distribution on
[0,100], which is dened as follows
F (v ) = Pr[i v ] =
v
v
.
100
1. What is th
Assignment 2: Econ 177
Professor Garratt
Consider the following two payment options:
Scenario A: A gamble that pays $100 with probability p and $0 with probability (1-p).
Scenario B: A payment of $C with probability 1.
In the table below, for each cash am
Assignment 1: Econ 177
In this assignment you use only the data from the first and second price auctions without
an entry fee or reserve price.
Part I: Second-Price Auction
First lets consider the 2 and 5-bidder second price auctions. For these auctions
o
Bidding Behavior
We assume people attempt to maximize their payo from participating in
an auction.
Hence, we are in a sense trying to determine their optimal bids.
However, an auction is a game in which the payo an individual earns
from any given bid depe
Expected Revenue
Here we calculate the expected revenue under the efficient equilibrium
bidding strategies for the first- and second-price auction formats.
In a first-price auction with F () uniform on [0,100], the symmetric
equilibrium bidding strategy h
A signal
Case
Case
Case
Case
1
2
3
4
Charlie Ricco
B signal
0
3
0
3
A's bid
0
0
3
3
B's bid
1.5
4.5
1.5
4.5
1.5
1.5
4.5
4.5
A's profit
Results from
-0.75 1000
-1.5 Trials
0
0.75
-0.375
-0.3795
Willliam Russell
Willliam Russell
All-Pay Auctions
In an all-pay auction, every bidder pays what
they bid regardless of whether or not they win.
Examples:
Elections
Almost any kind of contest or sports event
Research and Development
Wars
Lobbying
Since bids are wasted if you dont win,
Model I
The true value of the item being auctioned is v , but v is unknown to all
bidders.
Each bidder i receives a signal, si , about the true value, which is given by
the sum of the true value v and a random variable ei , which you should
think of as a
Model II
Common values can also be modelled as a special case of interdependent
values.
In the interdependent values model
v1 = s1 + s2
v2 = s2 + s1
where s1 and s2 are private signals of bidders 1 and 2, 0 is the weight
a bidder puts on her own signal an
Common Value Auctions
So far we have studied auctions for which bidders have private values.
In private value auctions each bidder knows how much she values the item,
and this value is her private information.
Now we will discuss common value auctions.
In
Optimal Auctions
We wish to analyze the decision of a seller who sets a reserve price when
auctioning o an item to a group of n bidders.
Consider a seller who chooses an optimal reserve for a second-price auction
with one bidder.
Clearly the seller who fa
SPA 2-bidder with $25 entry fee Winter 11
100
90
Number people who entered out when they should have stayed out:
Percentage of total:
0.15
80
Number people who stayed out when they should have entered:
Percentage of total:
0
70
Average Revenue:
36
0
53.13
SPA 2-bidder, Reserve = $50, Spring11
100
Average overbid: -11.5313
90
Number of Value Bids 92
Percent value bid:
0.3833
80
Number of bids within $1 of value bid: 109
Percent bids within $1 of value bid:
0.4542
70
Average Revenue: 35.93791
Bids
60
50
40
3
SPA 2-bidder Spring 2011
Average overbid:
100
-6.6855
Number of value bids:
Percent value bid:
89
0.3708
90
Number of bids within $1 of value bid:
Percent bids within $1 of value bid:
80
Average Revenue:
26.06775
Average earnings:
194.0725
70
Highest earn