Economics
Autor: Manpreet Singh Parmar • December 6, 2017 • Coursework • 2,104 Words (9 Pages) • 654 Views
Problem Set 8
Problem 1 – Vacation Auction (from Kreps).
Imagine you are taking part in an auction where the object being auctioned is a vacation trip. There are 15 other prospective buyers in addition to you. You have determined that the trip is worth $2000 to you: you would rather have the trip and pay some amount less than $2000 than to miss the trip and pay nothing, but you would rather miss the trip and pay nothing than take the trip if it costs more than $ 2000. You are indifferent between missing the trip and paying nothing and going on the trip and paying exactly $2000. So, your payoff is zero if you do not win the auction, and it is 2000-P if you win the trip and pay P.
You have very little idea how much the trip is worth to the other 15 bidders and how they bid.
- Suppose this is a first price sealed bid auction. Does the strategy of bidding $1950 weakly dominate the strategy of bidding $2000 for you? With the information provided can you compare bidding $1950 and bidding $1960? Can you compare bidding $2000 and bidding an amount more than $2000?
First price sealed bid auction: Here, we bid less than our actual valuation.
Payoff table for bidding $1950 or $2000 is:
NOT WIN
$1950 $2000
($50, 0) | ($50, 0) |
(0, 0) | (0,0) |
$1950
WIN
$2000
So, the payoff ($50) if we bid $1950 is more than 0 which is the payoff if we bid $2000.
Payoff table comparing 1950 and 1960
NOT WIN
$1950 $1960
($50, 0) | ($50, 0) |
($40, 0) | ($40, 0) |
$1950
WIN
$1960
Payoff ($50) for $1950 is more than payoff of $40 for $1960.
Payoff comparing $2000 and amount more than $2000
NOT WIN
$2000 More than $2000
(0, 0) | (0, 0) |
(-$$, 0) | (-$$,0) |
$2000
WIN
More than $2000
Payoff ($0) for $2000 is zero which is better than loss for > $2000.
- Suppose now this is a second price auction. Why does the strategy of bidding $2000 weakly dominate every other strategy for you?
In second price auction, bid will be for $2000 else would reduce chance of winning or Payoff will be 0.
NOT WIN
$2000 More than $2000
...