Pl Plan fo for T Today Fair division basics Intro to auctions
to split a heterogeneous want who 2people divisible good told to divide the cake into Player 1 is values 2 pieces she equally their favorite Player 2 picks G D Motel good is that player i has value is the V s S of cake fur piece Vico D I 1 1 on disjoint intervals additive value is are divisible values X there is a and CE Loi X YinX via evi set
rules to follow Are the incentivized players Uchoose protocol Iat of An A Ai Aa allocation An piece hatplayeri gets Ai alternative allocam Pareto optimal is YF no atleast as Bi ibn B sit every aggert is is strictly happier agent some happy not Paeto optimal choose Int ya PO is 1 cake give the whole define fairness How to are equally happy choose doesn't satisfy this both players Icut y ti is proportional th allocation Ai y v Aryan fi j rifAj if envy free Ai v EF proportional V j v CA viCAj s th h Ai v envifai l vifAj Is 0 I I proportional but 23 EF not 10 EET
Allocah Proportioned Claim Procedure is proportional K players left remaing whenever there are Proof each of them to In at least worth Cake is k Base case n Inductive step holds k left IH R
Ej msn.im sL Eval fxy3 x y Vi returns Vila yD e y set Cut returns x c Moving knife for n queries queries Cfnbgn 7 simple Doe conquer are necessary Wgn queries
1.5 4 4 OH
3 2h 1960 CB TJ 1995 AM 2016 203 cuts 4 h all n n n n n ch B n n et na
Auctions Singh item ancan bidders n Bidders private a value vi bidder has Fh rules specify b who wins m IEQ D gangampahpa First price auction bidder wins highest bid pay their highest bidder wins 2nd price anchor highest bid 2nd pay wins highest bidder All pay anch pays whattheybid every bidder utility Vi ythyoewqtp.fm pi iting poggi p 80 60 I 2 t 55
a 2nd price archer a dominant Thin In its bed truthfully to strategy bids g B maxghese PI else Fx everyone B 0 Vi Max bi Vi d Intfully rational individually who values bid it most welfare maximizing have higher total allocatn can other no auctioneer utility to the bidders ts a I Ii Ts another kimseeamb.dk i bidder only wants one each IRT is tmtnful that auction Design wegaemaximr.mg bid X 1 Try change everyone second highest not IR g Dst the itn highest bidder the Change ry bid
SO 8 5 3 tDsthghest the the winners T Charge bid 1st priori for every player for player i to bids mapping from rakes pi F N Vi player's value each that assure are public dishes and those probability Vi Uniffe too 2 players Va Va p Va yonepheynlij is value V bid How should when you you b PG b Prum Ufblv v Ku b Prf b VI b PrfVzL2b v G b food
b b max v b BME Bayes Nash Equilibrium BNR is pi Pa pre a E ufp Vi Ffv pi v I Efu Vb p ihr i b 1st price too Vi Va NV Efmox revenue ELanaanen too moxa vD L E J 2ndepny T mm µ by E E auctioneer revenue
Revenue equivalency Thin idf all drawn i values Set buyers of on which mechanism auction Than any the highest the bidder with object goes to the possible min win bidder the and Value ably 0 value has revenue the expected has sane papjgtmofbfdndnaw.ly Effvanchon exp 2players Ufo D 2nd price arch P EIFEFFEO Efik User Prayer V ftp.nceaveh 2 F fpagmtaeegb.dk't 2 BG Prf wins V v r U gD iEpg Al K k I Pauly P 2 Indu
Recommend
More recommend
