Multi-Agent Auction, Bidding and Contracting Support Systems

D.-J. Wu, Yanjun Sun

FMEC

May 11-12, 2000

Philadelphia

ABC in Human History

• Marrying daughter in ancient China using bidding, Song Dynasty

• Auction women as wives in Babylonia, Fifth Century, B.C.

• Farming contracting in ancient China, 452 B.C.

Auction Literature

• Tradition auction (single item)• English, Dutch• Sealed bid, open cry• First price winner and second price winner• Goods are storable

• Combinatorial auction (multi item)• iBundle (AuctionBot)

• Generalized Vickery auction

ABC in Information Economy (Adapted from Vakrat and Seidmann, 1999)

Business Model Auction Mechanism

Amazon-auctions.amazon.com (C2C)

Auction Platform Multiple-unit Uniform-price. Also dutch auctions

eBay-www.ebay.com (C2C)

Auction platform Multiple-unit discriminating price auctions. Also dutch auctions

OnSale-www.onsale.com (B2C)

Most goods are factory-direct

Multiple-unit, discriminating price auctions.

SurplusAuction-www.surplusauction.com (B2C)

Takes title on the goods it auctions

Multiple-unit, discriminating price auctions.

Persona-Logic

Firefly Bargain-

Finder

Jango Kasbah Auction-Bot

Tete-a-Tete

Product Brokering

Merchant Brokering

Negotiation

Developer PersonaLogic

MIT Anderson Consulting

Jango MIT Michigan MIT

Roles and Examples of Agent Systems as Mediators in Electronic Commerce (Adapted from Guttman, Moukas, and Maes, 1999)

eBAC Auction

Literature eBAC

Bid Discrete Continuous

Storability YES NO

Seller Single Many

Market One Two

Research Questions:

• Can artificial agents discover the equilibrium if it exists?

• Can artificial agents learn reasonably good policies when facing automated markets?

• What kind of mechanisms will induce coordination, cooperation and information sharing among agents?

Seller 1 Seller 2 Seller 3

Blackboard

Adaptive Learning

Seller 1Seller 2Seller 3

Figure XXX: Myopic Bidding System

Myopic Bidding System

Agents Learning in Myopic System

• Floating point representation.

• Identical initial population.

• Rule strength is current profit.

• Memory size = 1.

• Learning via genetic algorithms.

Model for Myopic Bidding

• Bidding Price

• Bidding Capacity

Maximize E x t x tX t

i i ii ( )

( ( )| ( )) 1

Maximize E L t L tL t

i i ii ( )

( ( )| ( )) 1

Technology and Capacity Parameters for the Three-Supplier Examples

i 1 2 3

Ex. 1 ci = Si + G(bi) 10 10 18

Ki 40 40 30

Price Bidding Model

Max E

x s G b

D x

Q Min D K

x s G b Q

xi

i i i

i i

i i i

i i i i i

i

( )

( )

[ , ]

[ ( )]

100

S1

18 55

S2 S2

18 55 18 55

S3

19 (328, 328, 1) (320, 0, 30) (0, 320, 30) (338, 338, 30)

55 (328, 328, 0) (320, 129, 80) (129, 320, 80) (737, 737, 454)

Nash Equilibria for Three-Supplier Normal Form Game

Capacity Bidding Model

Max E

p K L

p s G b Q p s G b L

Li

ii

ii

i i i i i i i

i

1

3

1

3

[ ( )] [ ( )]

Results: c = (10, 10, 18), K = (40, 40, 30)

Bidding Price Bidding Capacity

Path Independent

Pure YES. No co-op.

(18, 18, 19)

NO.

Mixed YES. No co-op.

(18, 18, 19)

YES. Co-op.

(27, 27, 19)

Path Dependent (Observed Average Profit)

YES. No co-op.

(18, 18, 19)

YES. Co-op.

(27, 28, 18)

Dynamic Pure Strategy Price Bidding, Path Dependent (Ex. 1)

0

5

10

15

20

25

30

35

40

Series1

Series2

Series3

Dynamic Pure Strategy Capacity Bidding, Path dependent (Ex. 1)

0

5

10

15

20

25

30

35

Series1

Series2

Series3

D xi i ( )77 D xi i ( )115 D xi i ( )100

ci

Ki

ci

Ki

ciKi

ciKi

ci

Ki

ci

Ki

  *

= 13, 13, 13= 30, 30, 30

PD (16, 16, 16) (30, 30, 30) (21, 21, 21)

PI (16, 16, 16) (30, 30, 30) (21, 21, 21)

= 11, 21, 21= 44, 23, 23

PD (21, 22, 22) (40, 31, 31) (No, No, No)

PI (21, 22, 22) (40, 31, 31) (No, No, No)

= 16, 16, 25= 34, 34, 22

PD (No, No, 26) (31, 31, 31) (No, No, No)

PI (No, No, 26) (31, 31, 31) (No, No, No)

= 7, 12, 17= 45, 26, 19

PD (No, No, 18) (39, 30, 30) (No, No, No)

PI (No, No, 18) (38, 30, 30) (No, No, No)

*=10,10,18=40,40,30

PD (No, No, 19) (No, No, No) (18, 18, 19)

PI (No, No, 19) (No, No, No) (18, 18, 19)

* =10,12,14=40,30,20

PD (14, 14, 15) (38, 29, 29) (No, No, No)

PI (14, 14, 15) (38, 29, 29) (No, No, No)

* Borrowed from WKZ.

Orthogonal Experiment

Summary of Myopic Price Bidding

• No cooperation exists under any climate.

• Bidding tends to have equilibrium under amenable climate.

• No difference between path dependent and independent.

Non-Myopic Bidding

• No learning (Fixed strategy tournament)

• One agent learning

• All agents learning

  Strategy Profit

1 (R, R, R) (17089, 14500, 5982)

 …   …   …

14 (N, N, N) (22091, 22091, 13623)

…   …   …

26 (T, T, N) (22091, 22091, 13623)

27 (T, T, T) (22091, 22091, 13623)

Tournament 1: Fixed Three-Strategy (Random, Nice, and Tit-for-Tat)

1 (R, R, R) (14718, 13427,7705)

  …  …   …

22 (N, N, N) (22091, 22091, 13623)

  …   …   …

42 (T, T, N) (22091, 22091, 13623)

43 (T, T, T) (22091, 22091, 13623)

  …   … …

64 (A, A, A) (10656, 10656, 934)

Tournament 2: Fixed Four-Strategy (Random, Nice, Tit-for-Tat, and Nasty)

Maximize Ex t

ii ( )

E x t x ti i t i it

, ( ( )| ( )),

1

30

One Agent Learning

… …     …

65 (G, R, R) (26356, 9842, 4143)

…   …   …

70 (G, N, N) (52800, 3857, 2379)

… …   …

75 (G, T, T) (23115, 21483, 13248)

…   …   …

80 (G, A, A) (17473, 5929, 9123)

Tournament 3: One Agent Learning

Strategy List 1 Strategy List 2 Strategy List 3

Seller 1 Seller 2 Seller 3

Strategy Discovery

Tournament

Figure XXX: Non-Myopic Bidding System

Tournament 4: All Agents Learning

Agent Learning in Non-Myopic System

• Representation: Each rule specifies multi-period bidding strategy.

• Randomly generated initial population.

• Rule learning via genetic algorithms.

• Rule strength is expected tournament profit.

Maximize Ex g t

ii ( , )

E

x g t x g t x g t

H Hi

i g t i j kt

T

k

H

j

H

, , ( ( , ), ( , ), ( , ))

111

Maximize Ex g t

jj ( , )

Ex g t x g t x g t

H Hj

j g t i j kt

T

k

H

i

H

, , ( ( , ), ( , ), ( , ))

111

MaximizeExgt

kk(,)

E

x g t x g t x g t

H Hk

k g t i j kt

T

j

H

i

H

, , ( ( , ), ( , ), ( , ))

111

Model for Non-Myopic Bidding

The Emergence of Trust

• Learning to cooperate

• Conditions for cooperation

• Impact of climate

0

10000

20000

30000

40000

50000

60000

0 50 100

Proportion of Nasty

Pro

fit

of

Seller

1

Random

Nice

T4T

Nasty

GA

Agent Learning in Dynamic Environment: Experiment 1

  1 2 3 4 5 6 7 8 9 10

0% 54 54 54 54 54 54 54 54 54 54

25% 54 54 54 54 54 54 54 54 54 54

50% 54 34 48 55 53 55 53 34 55 53

75% 54 34 55 39 34 55 39 34 55 39

100% 54 34 55 39 55 39 55 39 55 39

Agent Learning in Dynamic Environment, Experiment 2

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 25 50 75 100

Proportion of Nasty

Pro

fit

of

Seller

1

Profit Changing in Dynamic Environment, Experiment 2

Ongoing Research

• The ring of King Solomon• Agent communication

• Computational principles of trust• Agent coalition and Bargaining

• Role of Larmarcian learning

Summary• Artificial agents are viable in automated

marketplace.• Discover optimal bidding and contracting strategies in

the equilibrium if exist.• Find better strategies in a complex dynamic

environment where equilibrium do not exist.

• The emergence of trust.• Depends on the auction mechanism: Capacity bidding

induces cooperation.• Non-myopic bidding leads to cooperation while myopic

bidding does not.• Climate has impact on agents cooperation.