Auctions Flashcards
Auction
Selling of a good or service by asking buyers to announce the amount they are willing to pay.
Why use auctions (1 pro)
Most markets are imperfect and valuation differs between buyers, so allow sellers to discover buyers’ true valuation.
Two parameters of auctions
Nature of the good
Rules of bidding
Nature of the good : 2 types
Private value auctions
Common value auctions
Private value auctions
Each consumer has a own private value (one mans trash another mans treasure)
Common-value auctions, and example
The good auctioned is worth the same for all consumers, even if they have different valuations. (E.g drilling rights for oil companies)
The value is the same for all buyers, but their estimation of the value may differ (e.g one company may need it more so value it more, however the real value is the same)
2nd parameter of auctions:
Types of bidding rules : standard private-value auctions (4)
English
Dutch
Sealed-bid auction
Vickrey auction or philatelist auction
English auction characteristics (2) (most traditional)
Open outcry (public info)
First-price ascending auction (sellers start with reserve price - the lowest price the seller will agree to receive) then bid in increments until last bidder.
Dutch auction (3)
Quick (people buy before others get)
Open outcry (public)
First price descending auction - starts with a high price, lowered until buyer is willing to buy.
Sealed-bid auction (3)
First price auction
Each bidder states price without revealing to other bidders (e.g writes bid on paper) , prices are only observed by the organisers, and so good goes to highest bidder (provided if above reserve price)
So we also consider price others might be bidding to, so bid more. (Good for sellers, bad uncertainty for buyers)
Vickrey auction or philatelist auction
A variant of sealed bid auction, with a twist : 2nd price auction
Each bidder states price without revealing it to other bidders. Good is awarded to the last bidder who pays the second-highest price!! NOT THEIR PRICE WHICH WAS THE TOP
Makes it more efficient for the buyer as not overpaying. Seller agrees since they want people to come back so make it more rational for buyers ; (people won’t return if overpaid)
Japanese variant of the English auction
Price rises are increased with a timing mechanism
Auction design: 2 goals they want to achieve
Profit maximisation (for seller)
Pareto efficiency
What does pareto efficiency mean in an auction
The good is allocated to the buyer with the highest value of the bid
Is the English auction with no reserve price pareto efficient
What about with a reserve price?
Yes - the highest bidder wins (no reserve price to meet)
Not always - as if highest bidder is still below the starting reserve bid, the exchange will not take place.
Example of this:
Suppose 2 bidders participating in an English auction (NO RESERVE PRICE) with increment bid of 1.
Seller believes the valuation of each bidder is 20 at 50% chance, and 50 at 50% chance.
A) What are the possible situations, and at what probability of each?
B) What are the winning bids, and probability
C) Expected value to seller
D) Now use a reserve price of 50. What happens to EV, what can we conclude?
4 possible situations occurring with 25% chance:
(20; 20), (20 𝑜𝑟 21; 50), (50; 20 𝑜𝑟 21), (50; 50).
2nd & 3rd situations are depending on who starts the bidding first.
B) So 4 different winning bids with 25% chance of each.
20;20 WB=20 (since no one goes above to 21 since same private valuations)
20 or 21;50 WB=21 (it will be whoever bids 21)
50;20 or 21 (it will be whoever bids 21)
50;50 will be 50 as no one goes above to 51 as have same private valuations
C) Expected value to seller is…
E[V) = (20 x 0.25) + (21 x 0.25) etc = 28
D) Now there is a 25% chance of no sale, and 75% winning bid is 50. Since 20;20 situation is removed from possibility.
EVr = 0 x 0.25 + 50 x 0.75% = 37.5
So EV is higher with the reserve price, however a loss of efficiency (25% no trade)
Are Dutch auctions pareto efficient?
Not always - since bidders do not know each others valuations, and the auction starts at a very high price, the bidder with the highest valuation may wait to long and thus lose to the lower bidder.
(Since they may try get away by waiting for it to get lower, but it gets snapped up)
Are sealed-bid first price auctions pareto efficient?
Not always - bidders do not know each others valuations, so the bidder with the highest valuation may bid too low and lose to another bidder
(Try pay lower than what they are willing to actually pay, and lose out)
Are sealed-bid second price auctions Pareto efficient?
Yes - as design of auction makes it rational and avoids overpaying. (Goes to 2nd highest bidder)
Use a sealed-bid second price (Vickrey) auction to prove pareto efficiency
Suppose two bidders with respective true valuations v₁ and v₂, and respective bids b₁ and b₂.
A) What is bidder 1’s expected gain?
B) What is the intuition behind maximising gain, using v₁ &b₂?
C) What is the main conclusion
A) Expected gain for bidder 1 is
E[G₁] = (v₁-b₂) Pr(win) + 0Pr(lose) = (v₁-b₂)Pr(b₁>b₂)
Difference between valuation of bidder 1 and bidder 2’s bid is the gain (v₁-b₂)
And only win if their bid is higher than 2nd bidder (b₁>b₂) so we look at the probability of that too Pr(b₁>b₂)
B)
If v₁>b₂ probability of winning should be maximised, so set b₁=v₁ (set their bid equal to their valuation since want to win)
If v₁<b₂ probability of winning should be minimised, so set b₁=v₁ (set their bid equal to their valuation since want to lose)
C) Using true valuations despite not knowing each others’ valuation is rational!
Other private value auctions
Escalation auction
Everyone pays auction (lobbying) - but only highest wins
EBay auctions - problem - late bidding
Position auctions
2nd nature of good:
Common-value auctions
Good has same value for all buyers/bidders
But their estimation of the value may vary.
How do we write the estumated value
E[Vi] = v + εi
V is common value for all
εi is error term indiviudal εi estimation
If each bidder bids the amount of their true valuation, who wins
The one with the highest error term.
I.e pays more than the true value of v !!
What is this known as?
The winners curse
Winners curse expression
What does this indicate?
V + εmax > v
The winning bidder was overoptimistic.
What is optimism like in a common-value action with more bidders
The highest bidder would need to be super optimistic to win and thus price will likely be significantly higher than the value (v) so overpay
So more bidders, the better it is to be less optimistic
Problems with auctions (3)
Subject to manipulations and collusions - inefficient
We have assumed bidders are committed to their own bid (may be unrealistic as bidders sometimes drop out)
Sellers can manipulate actions with fictitious bids to inflate the price (market manipulation)
Mechanism design : 2 types of decisions to take when designing
Type of signal from one agent to another
Rules of how outcome is determined
Things to be considered in design (4)
Resource constraint
Voluntary vs mandatory participation
How agents communicate
Selfishness of agents - incentive compatability constraint - act in own best interest.
