Fair Division
Fair Division • What is a fair way for 2 people to split a heterogenous, divisible good? • Why not 50/50? • I Cut, You Choose Protocol • Player I told to split the good into two pieces A and B such that v(A) = v(B) = ½ v(A U B). • Player II picks his favorite of A and B. • Player I takes the other piece.
Formal Model it
is An proportional Ai Aa Allocation th ti Ai f v Ai pieceplayer i gets 4 Aj Ai envy free y ti j v hcqFeries talent Standardmedel e is thru 2 types of queries Vi's access to playerintms Vi B x y Eval cut 042 Cut Kia queries qq.mjggy.IE
division protocol of a How to complexity measure as fn of running fine n wanti Standard model e 2 types of queries i's is thru player i returns Vicky x y Eval cut his I't's protocol take does a How many queries 2gueries Yon Choose Cut I can get proportional duc de conquer With queries n woc.us
Is 3
al as 4 I 04 i s s
O O cY3 Bu
5 queries syandge 3 A donug 1960 Taylor Brans 1995 4 n even h 3 ab no upper bound on main EEE.E.es McKenzie Aziz 2016 cuts 4 1203 h protocol for anyn n n n cuts n best loner bounds unsythn
C Truthfulness player can T Fis truthful y no by misrespondig to utility for outcome their any query Randomized grech is tmthff gne player cant by misresponding their expected utility deterministic mech for awaiting No Thm_ truthful is proportional not even approx Thin IT Turgut pashm Bn B nonconstructive
3 tmhflinexpm arkatepettndompahtfpdaynasssfrnbmdts in exp Truthful G CD at random assigned A partition of bundles are th Exp whhty Yn t
indivisible division with Fair gqhq.gg qq.gg for item j j m Fh i Oo o K I doesnt why o i envy k od I
one good Efcpto Au is Aa Album y one good to neb up F good g C Ak set Fk Fi 2 players vifAkg Vitti i as share Maximin of player follows pahhous goods into ingroups i Bn B Bj v tales min i M that panda inputs where no MMS i agenti each guarantees P MMS 34 3 can generate
A
Auctions • Ancient mechanism for buying and selling goods. • In modern times, used for many economics transactions. • In the age of the Internet, we can buy and sell goods and services via auctions online, e.g. using eBay • Companies. like Google and Microsoft use ad auctions to sell advertisement slots that will appear alongside your search results. • All major search engines and social networking sites (e.g. Facebook) make most of their money from running real-time auctions used to sell online advertisements. • Consequence: auctions are a major driver of modern Internet economy. • Why use an auction as opposed to simply fixing prices?
Why might a sell user an auction as opposed to fixing a price? • Because sellers don’t know how much buyers value their goods and don’t want to risk setting prices that are too low (leaving money on the table) or too high (nobody buys). • Auction is technique for dynamically setting prices. • In Internet settings, where the participants in the auction are computer programs or individuals who don’t know each other, price- setting is particularly difficult and this is what motivates auctions.
auctions item Single single good Seller w bidders strategic h rulesspecify b who wins Rhofumbuffderpass yn for the value bidder has a private each itembergsoldT 3 standard types highest bidder TEETH das ftp.riceanchm FE y w'wia Erik m Igf a highestbidder wins All pay anch everyone pays what they bid anchor 2nd pence anchor eBay Vickrey anchen sealed bids y submit a dominant d is Ina Lemma s vi set bi ie truthfully bid to Dsl C gy compatible dominant strategy incentive B b i let IIB bids h.gg Fix Proof bjbeddigsmuhyhTegtiaa Ees nmghp e
chievesths Y tmhfully don't to need cod agents Truthful strategize Hen ends that 2ndprice anchor guarantees who the player hands of up in the the most it Valves welfare surplus efficiency social of all participants utilities of sum anchrees viIiwm PDta f including vi twitter.mu f fEfeu
Recommend
More recommend