w7 auctions

Question 1

why are auctions useful in ai decision making

Answer 1

they are good for effecitly distributing resources among competing agents

helps provide a framework for agents to make decisions based on their values and needs

creating a well designed auction encourages truthful bidding and not manipulation

its a part of mechanism design

Question 2

what is mechanism design

Answer 2

design rules such that the strategies the players develop lead to desierable outcomes, you want agents to tell the truth so make that strategy beneificial

ie in soccer, make the rules such that the players dont think its smart to shoot on their own goal

Question 3

what are the types of auctions

Answer 3

single item auction

multi item auction

Question 4

what are the types of signle item auctions

Answer 4

english, dutch, sealed-bid first price, sealed-bid second price (Vickery Auction)

the best auction designs are
vickery with reserved price and myersons optimal uaction

Question 5

what is the english auction

Answer 5

bids start low and progressivly get higher and stops until no one else bids higher

the item is always sold to the highest bidder
and the auctioneeers revnnue is maximized

but this is given they follow the strategy of increasing the price little by little until it exceeds a max value

there is a dominate strategy but it depending on how others play

Question 6

is there a dominat startegy in english auction

Answer 6

there is a dominate strategy but it depending on how others play

Question 7

what is a dutch auction

Answer 7

the auctionear starts off by annoucing a unreasoable high price and lowers it until someone agrees to the price

the strategy is to place a bid when the price becomes appropriate otherwise the agent risks overpaying for the product

the auctionneers revenue is also not nesseciarly maximized

Question 8

is there a dominate strategy in dutch auction

Answer 8

there is no dominant strategy and the item is not always sold to the highest bidder

Question 9

what is a sealed-bid first price auction

Answer 9

a blind auction where bids are sealed in an envelop and the agent with the higest bid wins

there is no dominant strategy

Question 10

how do you maximize expected utilited in a sealed bid first price auction

Answer 10

you think the item has a certain value and your goal is to choose a bid thats lower than your value but high enough so you still get the item

ur utility is quasi-linear (idk if this is important)

suppose ur value of item is v = 30

and utility u = v - p, p is how much you pay

so if you bid your value u will get no utility bc then u paid too much :C

so estimate how others may bid and try to find a balence using probability

suppose other agents bids follow uniform distrbution of U(10,40)

expected utility, where b = ur bid price (p basically is also b):

E[u] = Pr(win) x (v - p)

= (b -10/ 40-10) x (30 - b)

maximize this function -> max E[u]

thus b = 20

Question 11

what is sealed-bid second price auction (vickrey auction)

Answer 11

bids are hidden, and the item is given to the highest bidder but they are charged the price of the second highest bid

the dominant strategy is to bid truthfully (bid the value you think the item is worth)

Question 12

why are truthful auctions desireable

Answer 12

knowledge about other bids is ireelevant
easier for bidders to make a strategy
easier for auctioneers to predict the outcome

truthfulness is also called incentive compatible

Question 13

prove vickery auction is truthful

Answer 13

watch a youtube video

Question 14

how can we figure out how to maxmize revenue

Answer 14

revelation principle, strategic equivalence, renvenue eqivalence

Question 15

what is the revelation principle

Answer 15

a complicated system can always be simplified into one where truth-telling is the best strategy for every participant

Question 16

what is direct vs indirect mechanism

Answer 16

direct is you do it all at once
- ie submit everything then analyze then return output

indirect is overtime
- ie submit one at a time and information is revaled over time and analyze repeatedely

like vickery auction vs english auction respectivly

Question 17

why is the revlation principle important

Answer 17

indirect mechnaisms are more complicated than direct mechnaismis so we need a way to simplify mechnanisms

for analysis purposes we can only consider truthful mechanisms
and because of this principle we know that there is a truthful mechanisms (direct)

Question 18

why may someone prefer indirect to direct/truthful mechanismm

Answer 18

while more complicated indirect mechnaisms are more private, some agents wont comprimise on that

Question 19

what is stategic equivalence

Answer 19

that two situations (or games) are essentially the same in terms of strategy, even if they look different.

Two games are strategically equivalent if:

The players’ choices and preferences lead to the same outcomes.

The payoffs in one game can be transformed into the payoffs of the other game by a simple mathematical rule (like scaling or adding a constant)

Question 20

what is revenue eqiuvalence

Answer 20

if certain conditions are met, all auction formats will generate the same expected revenue for the seller, as long as bidders behave rationally and truthfully.

Question 21

wehat is the opitmal auction

Answer 21

vickrey auction with reserved price

the acutioneer chooses a threshold price r and if the highest bid is greater than r the item is given to him

the bidder is charged the max either r or the second highest bid

if r is not reached then auctioneer keeps the item

Question 22

how does mysersons optimal auction help auctioneers

Answer 22

Imagine you’re selling a rare collectible:

You estimate that the bidders’ valuations are distributed in a certain way.

Myerson’s method helps you decide:

What minimum price (reserve price) to set.

How to pick the winner (not just based on the highest bid, but based on the adjusted virtual valuation).

Using these steps, you ensure you’re getting the best possible revenue on average

Question 23

what is bulow-klemperer theorem

Answer 23

setting up an opitmal auction irl is costly and time consuming

so bulow-klemperer theorem suggests to attract more bidders rather than learning the perfect auction distributions

because it shows that expected utitlited of the vickery auction with more bidders is greater than the optimial revenue in mysersons auction with less bidders