Durable good: Buy at t=1 or wait until t=2?
Durable good: Buy at t=1 or wait until t=2?
Non-Durable good: Buy once and hold or buy in each period?
x j
xi

n
n
0
 xi   j 1 ( p j  mc(i ))
 xi   j 1 ( p j  mc(i ))
pi
pi
p j
N bidders, K units (prizes)
Bidders submit bids under some format
Bids are ranked based on some rule, this ranking determines the allocation
Prices are set based on some rule
N bidders, K units (prizes)
[who can participate, how many prizes]
Bidders submit bids under some format
[“bid language”, timing, confidiential/not, etc.]
Bids are ranked based on some rule, this ranking determines the allocation
Prices are set based on some rule
[tons of flexibility]
N bidders, 1 unit for sale
Bidders submit sealed (secret) bids (i.e. other bidders cannot observe), think
of this as putting bids in sealed envelopes which the auctioneer collects
Auctioneer opens the bids, the highest bidder wins and pays bid
How would you bid in this auction?
Value of acquiring the good 𝒗𝒊 for person 𝒊
Utility if win: = 𝒗𝒊 − 𝒃𝒊𝒅𝒊 , if lose=0
Dynamics & incentives
•
•
•
Never want to bid more than value
Increasing bid raises chance of winning, but lowers utility of one wins
How would you bid?
Many complicated equilibria (beyond scope of course), but intuition is
straightforward
Generally, I want to shade my bid below my value and I shade more when
there are more bidders, because I need to beat more people
How I bid will depend on what I know about other’s valuations (and what I
don’t know)
N bidders, 1 unit for sale
Bidders submit sealed (secret) bids (i.e. other bidders cannot observe), think
of this as putting bids in sealed envelopes which the auctioneer collects
Auctioneer opens the bids, the highest bidder wins and pays the bid of the
second highest bidder
Utility if win: = 𝒗𝒊 − 𝒎𝒂𝒙(𝒃𝒊𝒅−𝒊 ), if lose=0
Important: bidding higher increases chance of winning, but not the price
paid
What would you bid?
Never bid more than value
Imagine a bid less than value
• Currently winning  raising bid does not raise price paid
• Currently losing  raising bid increases chance of winning
Equilibrium is everyone bids value
Never bid more than value
Imagine a bid less than value
• Currently winning  raising bid raises price paid
• Currently losing  raising bid increases chance of winning and price paid
Equilibrium is everyone shades bid below value
Start with bid at reserve price
“Cry out” to make bid above current bid (has to be minimum above
previous)
Auction ends when no bidder wants to exceed current highest
Simple rule: bid until reach value, then sit out
Very likely highest value player will win (certain under certain assumptions)
If bids are linked to identities, can be an issue if one bidder is thought to be
particularly knowledgeable about the value
Although you don’t bid value, outcomes should be similar to sealed bid
second price auction (highest value bidder pays second highest value)
Minimum bid required to win auction
If all bids are below reserve, item does not sell
You can think of reserve price as the bid of the auctioneer, so in a second
price auction it would correspond to auctioneer’s value
Reserve prices can be incredibly important when the number of bidders is
small
Uncertainty over value of item
Instead of doing complicated optimal price calculation, let “market decide”
Auction can be thought of as a price (reserve) + potential to gain more if
value is higher
If you really want to sell the time, your reserve price will be 0 and the item
will sell as long as someone values it
Asset markets: “simultaneous double action”
Projects (e.g. build a bridge, build a rocket): “procurement auctions”
Land (e.g. oil leases, logging rights, houses)
Spectrum: “ascending clock auction” or “combinatorial auction”
Asset markets: “simultaneous double action”
Projects (e.g. build a bridge, build a rocket): “procurement auctions”
Land (e.g. oil leases, logging rights, houses)
Spectrum: “ascending clock auction” or “combinatorial auction”
Consumer retail (even eBay has moved mostly to buy it now)
Healthcare
Education (e.g. your tuition)
Posted prices seem to prevail in most goods consumers buy (although
sometimes there is an “auction underneath”, e.g. who is the recommended
buyer on Amazon)
There are many bidders who show up to the auction
Bidders do research on value of the good/prize
Screening mechanisms or legal recourse that ensure bidders can pay when
they win or live up to terms of the contract of winning
You want to give the good(s) to the highest bidder (may not want to for
fairness reasons)
Please read the Klemperer article
Collusion among the bidders
Not enough bidders (entry deterrence)
Most bidders don’t win, but are essential in propping up the price
But why should they show up if they know they won’t win?
Costly entry (e.g. do research on products, travel to auction, etc.)
Auctions that give many competitors a chance to win are a solution to this
problem (sealed bid auctions or bidder subsidization)
Auctions, like markets generally, rely on bidders competing with each other
Bidders want to make deals and play lower prices
This is especially a problem in repeated auctions (e.g. I let you win this week,
you let me win next week)
Collusion can often happen via signaling, not “let’s cheat emails”
Block of spectrum: channel(s) of electromagnetic spectrum, e.g. a TV
channel or the equivalent in the higher bands that gives right to use that
spectrum in a defined physical area. Multiple bidding rounds.
Germany auctioned 10 blocks
Mannesman’s first round bid:
Blocks 1-5: 18.18 million
Blocks 6-10: 20 million
18.18*1.1 =20 (10% increase)
4 licenses, 4 incumbents
Problem with ascending auction  potential entrants will assume that the 4
incuments will eventually win, not bother entering
Solution: “Anglo-Dutch Auction” (ascending auction until 5 bidders remain,
then sealed bid auction)
When a 5th license became available, used standard ascending auction
made sense as it was guaranteed one new entrant would get a license
5 licenses, 5 incumbents
Used ascending auction  problem entrants have little incentive to show up
Reserve prices were not set aggressively enough
In the end, raised 70% less per capita than UK auction
Auctions are the standard economic mechanism for price and value
discovery
Auctions work well when certain pre-conditions are met
They work poorly in other conditions, and in this case reserve prices function
to clear the market and it is very similar to standard pricing case