w7 auctions Flashcards
why are auctions useful in ai decision making
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
what is mechanism design
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
what are the types of auctions
single item auction
multi item auction
what are the types of signle item auctions
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
what is the english auction
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
is there a dominat startegy in english auction
there is a dominate strategy but it depending on how others play
what is a dutch auction
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
is there a dominate strategy in dutch auction
there is no dominant strategy and the item is not always sold to the highest bidder
what is a sealed-bid first price auction
a blind auction where bids are sealed in an envelop and the agent with the higest bid wins
there is no dominant strategy
how do you maximize expected utilited in a sealed bid first price auction
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
what is sealed-bid second price auction (vickrey auction)
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)
why are truthful auctions desireable
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
prove vickery auction is truthful
watch a youtube video
how can we figure out how to maxmize revenue
revelation principle, strategic equivalence, renvenue eqivalence
what is the revelation principle
a complicated system can always be simplified into one where truth-telling is the best strategy for every participant
what is direct vs indirect mechanism
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
why is the revlation principle important
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)
why may someone prefer indirect to direct/truthful mechanismm
while more complicated indirect mechnaisms are more private, some agents wont comprimise on that
what is stategic equivalence
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)
what is revenue eqiuvalence
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.
wehat is the opitmal auction
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
how does mysersons optimal auction help auctioneers
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
what is bulow-klemperer theorem
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
