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ECON30290 - Auction Theory
创建日期：2024-05-10 15:51:34
所属分类：经济Economics
标签： ECON30290
Auction Theory

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ECON30290 - Auction Theory

Unit 2 - The Revenue Equivalence Theorem
Omer Edhan
Omer Edhan 1 / 29 1 / 29
Section 2.1: Revenue Equivalence
for 1st and 2nd Price Auctions
Omer Edhan 2 / 29 2 / 29
Section 2.1A: Payment and
Revenue in 1st Price Auction
Omer Edhan 3 / 29 3 / 29
1st Price - Payment and Revenue
Buyer i with valuation x expected payment:
mI (x) = Pr(Win)× Bid
= G (x)× E [Yi |Yi ≤ x ]
Seller’s expected revenue:
e I
=
n
∫ v
v
mI (x)
f (x)dx
Omer Edhan 4 / 29 4 / 29
1st Price - Payment and Revenue
Buyer i with valuation x expected payment:
mI (x) = Pr(Win)× Bid
= G (x)× E [Yi |Yi ≤ x ]
Seller’s expected revenue:
e I
=
n
∫ v
v
mI (x)
f (x)dx
Omer Edhan 4 / 29 4 / 29
1st Price - Payment and Revenue
Buyer i with valuation x expected payment:
mI (x) = Pr(Win)× Bid
= G (x)× E [Yi |Yi ≤ x ]
Seller’s expected revenue:
e I
=
n
∫ v
v
mI (x)
f (x)dx
Omer Edhan 4 / 29 4 / 29
1st Price - Payment and Revenue
Buyer i with valuation x expected payment:
mI (x) = Pr(Win)× Bid
= G (x)× E [Yi |Yi ≤ x ]
Seller’s expected revenue:
e I
=
n
∫ v
v
mI (x)
f (x)dx
Omer Edhan 4 / 29 4 / 29
1st Price - Payment and Revenue
Buyer i with valuation x expected payment:
mI (x) = Pr(Win)× Bid
= G (x)× E [Yi |Yi ≤ x ]
Seller’s expected revenue:
e I
=
n
∫ v
v
mI (x)
f (x)dx
Omer Edhan 4 / 29 4 / 29
1st Price - Payment and Revenue
Buyer i with valuation x expected payment:
mI (x) = Pr(Win)× Bid
= G (x)× E [Yi |Yi ≤ x ]
Seller’s expected revenue:
e I =
n
∫ v
v
mI (x)
f (x)dx
Omer Edhan 4 / 29 4 / 29
1st Price - Payment and Revenue
Buyer i with valuation x expected payment:
mI (x) = Pr(Win)× Bid
= G (x)× E [Yi |Yi ≤ x ]
Seller’s expected revenue:
e I =
n
∫ v
v
mI (x)f (x)dx
Omer Edhan 4 / 29 4 / 29
1st Price - Payment and Revenue
Buyer i with valuation x expected payment:
mI (x) = Pr(Win)× Bid
= G (x)× E [Yi |Yi ≤ x ]
Seller’s expected revenue:
e I = n
∫ v
v
mI (x)f (x)dx
Omer Edhan 4 / 29 4 / 29
Section 2.1B: Payment and
Revenue in 2nd Price Auction
Omer Edhan 5 / 29 5 / 29
2nd Price - Payments and Revenue
Under a symmetric equilibrium β(x) = x (bid the valuation).
Bidder 1 with valuation x has expected payment:
mII (x)
= Pr(Win)× E [2nd bid |x is highest]
= G (x)× E [Yi |Yi < x ]
= mI (x)
Seller’s expected revenue:
e II
= n
∫ v
v
mII (x)f (x)dx = n
∫ v
v
mI (x)f (x)dx = e I
.
Omer Edhan 6 / 29 6 / 29
2nd Price - Payments and Revenue
Under a symmetric equilibrium β(x) = x (bid the valuation).
Bidder 1 with valuation x has expected payment:
mII (x)
= Pr(Win)× E [2nd bid |x is highest]
= G (x)× E [Yi |Yi < x ]
= mI (x)
Seller’s expected revenue:
e II
= n
∫ v
v
mII (x)f (x)dx = n
∫ v
v
mI (x)f (x)dx = e I
.
Omer Edhan 6 / 29 6 / 29
2nd Price - Payments and Revenue
Under a symmetric equilibrium β(x) = x (bid the valuation).
Bidder 1 with valuation x has expected payment:
mII (x)
= Pr(Win)× E [2nd bid |x is highest]
= G (x)× E [Yi |Yi < x ]
= mI (x)
Seller’s expected revenue:
e II
= n
∫ v
v
mII (x)f (x)dx = n
∫ v
v
mI (x)f (x)dx = e I
.
Omer Edhan 6 / 29 6 / 29
2nd Price - Payments and Revenue
Under a symmetric equilibrium β(x) = x (bid the valuation).
Bidder 1 with valuation x has expected payment:
mII (x) = Pr(Win)× E [2nd bid |x is highest]
= G (x)× E [Yi |Yi < x ]
= mI (x)
Seller’s expected revenue:
e II
= n
∫ v
v
mII (x)f (x)dx = n
∫ v
v
mI (x)f (x)dx = e I
.
Omer Edhan 6 / 29 6 / 29
2nd Price - Payments and Revenue
Under a symmetric equilibrium β(x) = x (bid the valuation).
Bidder 1 with valuation x has expected payment:
mII (x) = Pr(Win)× E [2nd bid |x is highest]
= G (x)× E [Yi |Yi < x ]
= mI (x)
Seller’s expected revenue:
e II
= n
∫ v
v
mII (x)f (x)dx = n
∫ v
v
mI (x)f (x)dx = e I
.
Omer Edhan 6 / 29 6 / 29
2nd Price - Payments and Revenue
Under a symmetric equilibrium β(x) = x (bid the valuation).
Bidder 1 with valuation x has expected payment:
mII (x) = Pr(Win)× E [2nd bid |x is highest]
= G (x)× E [Yi |Yi < x ] = mI (x)
Seller’s expected revenue:
e II
= n
∫ v
v
mII (x)f (x)dx = n
∫ v
v
mI (x)f (x)dx = e I
.
Omer Edhan 6 / 29 6 / 29
2nd Price - Payments and Revenue
Under a symmetric equilibrium β(x) = x (bid the valuation).
Bidder 1 with valuation x has expected payment:
mII (x) = Pr(Win)× E [2nd bid |x is highest]
= G (x)× E [Yi |Yi < x ] = mI (x)
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MATH20602 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 MAS316/414 ACCT2522 MSIN0181 ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 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