Auctions

Question 1

Auction

Answer 1

Selling of a good or service by asking buyers to announce the amount they are willing to pay.

Question 2

Why use auctions (1 pro)

Answer 2

Most markets are imperfect and valuation differs between buyers, so allow sellers to discover buyers’ true valuation.

Question 3

Two parameters of auctions

Answer 3

Nature of the good

Rules of bidding

Question 4

Nature of the good : 2 types

Answer 4

Private value auctions

Common value auctions

Question 5

Private value auctions

Answer 5

Each consumer has a own private value (one mans trash another mans treasure)

Question 6

Common-value auctions, and example

Answer 6

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)

Question 7

2nd parameter of auctions:

Types of bidding rules : standard private-value auctions (4)

Answer 7

English
Dutch
Sealed-bid auction
Vickrey auction or philatelist auction

Question 8

English auction characteristics (2) (most traditional)

Answer 8

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.

Question 9

Dutch auction (3)

Answer 9

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.

Question 10

Sealed-bid auction (3)

Answer 10

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)

Question 11

Vickrey auction or philatelist auction

A variant of sealed bid auction, with a twist : 2nd price auction

Answer 11

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)

Question 12

Japanese variant of the English auction

Answer 12

Price rises are increased with a timing mechanism

Question 13

Auction design: 2 goals they want to achieve

Answer 13

Profit maximisation (for seller)

Pareto efficiency

Question 14

What does pareto efficiency mean in an auction

Answer 14

The good is allocated to the buyer with the highest value of the bid

Question 15

Is the English auction with no reserve price pareto efficient

What about with a reserve price?

Answer 15

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.

Question 16

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?

Answer 16

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)

Question 17

Are Dutch auctions pareto efficient?

Answer 17

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)

Question 18

Are sealed-bid first price auctions pareto efficient?

Answer 18

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)

Question 19

Are sealed-bid second price auctions Pareto efficient?

Answer 19

Yes - as design of auction makes it rational and avoids overpaying. (Goes to 2nd highest bidder)

Question 20

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

Answer 20

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!

Question 21

Other private value auctions

Answer 21

Escalation auction

Everyone pays auction (lobbying) - but only highest wins

EBay auctions - problem - late bidding

Position auctions

Question 22

2nd nature of good:

Common-value auctions

Answer 22

Good has same value for all buyers/bidders

But their estimation of the value may vary.

Question 23

How do we write the estumated value

Answer 23

E[Vi] = v + εi

V is common value for all
εi is error term indiviudal εi estimation

Question 24

If each bidder bids the amount of their true valuation, who wins

Answer 24

The one with the highest error term.

I.e pays more than the true value of v !!

Question 25

What is this known as?

Answer 25

The winners curse

Question 26

Winners curse expression

What does this indicate?

Answer 26

V + εmax > v

The winning bidder was overoptimistic.

Question 27

What is optimism like in a common-value action with more bidders

Answer 27

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

Question 28

Problems with auctions (3)

Answer 28

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)

Question 29

Mechanism design : 2 types of decisions to take when designing

Answer 29

Type of signal from one agent to another

Rules of how outcome is determined

Question 30

Things to be considered in design (4)

Answer 30

Resource constraint

Voluntary vs mandatory participation

How agents communicate

Selfishness of agents - incentive compatability constraint - act in own best interest.