An Extended Alternating-Offers Bargaining Protocol for Automated Negotiation in Multi-agent Systems P. Winoto, G. McCalla & J. Vassileva Department of.

An Extended Alternating-Offers An Extended Alternating-Offers Bargaining Protocol for Automated Bargaining Protocol for Automated Negotiation in Multi-agent SystemsNegotiation in Multi-agent Systems

P. Winoto, G. McCalla & J. VassilevaDepartment of Computer Science

University of Saskatchewan

Presented by

Julita Vassileva

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Automated Negotiation in Multi-agent Systems (MAS)

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$100 $1

• Cooperative behavior in competitive situation

• Conflict of interest

My agent will negotiate with you

• Applications: distributed problem solving, resource allocation, e-commerce

Classification of Negotiation

Protocols:– auctions– bargaining– voting, etc.

Negotiated Items:– single attribute (e.g. price)– multiple attribute (e.g. price and quality)

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Auctions

Very efficient, but:

– Scheduled in advanced

– Non-negotiable

– Only for price

– Controlled by auctioneer

Alternative: Bargaining!!

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Bargaining

• Axiomatic bargaining– Bargainers provide information (proposals, facts, and other

arguments)– Arbitrator sets axioms– Arbitrator decides outcomes (guaranteed)– E.g. Egalitarian bargaining solution, Nash bargaining solution,

etc.

• Strategic bargaining– Set a protocol, both bargainers agreed on it– Start bargaining (Bargainers offer proposals)– Bargainers decide final outcomes (not guaranteed)– E.g. alternating-offer bargaining

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Alternating-offer Bargaining

Scenario 1:Buyer: How much?

Seller: $1000.

Buyer: $500?

Seller: $800.

Buyer: $600?

Seller: $700!

Buyer: OK, $700.

Scenario 2:Buyer: How much?

Seller: $1000.

Buyer: $10.

Seller hangs up the phone.

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Buyer’s acceptable setBuyer’s acceptable set

Seller’s acceptable setSeller’s acceptable set

Alternating-offer Bargaining Space: an Example

00

seller’s private seller’s private valuationvaluation(Seller indifferent (Seller indifferent between two point between two point in this line)in this line)

buyer’s buyer’s private private valuationvaluation

Unit Unit priceprice

qualityquality

Feasible Feasible set set

possible solutions here

No solution here

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Seller’s proposal

start from here

Buyer’s proposal

start from here

Alternating-offer Bargaining

• Bargaining problem: <X, D, 1, 2>– X: feasible set – D: disagreement : preference order of bargainers 1 and 2.

• Goal: achieve xX • Solving method: backward induction (Game-

theoretic approach)• Assumptions:

– Perfect rationality– Perfect foresight

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Modifications:

• Asymmetric information (Mudgal & Vassileva, 2000)

• With deadline (Sandholm & Vulkan, 1999)

• Argumentation (Jennings et. al., 2001)

• Strategic delay (Cramton, 1992)

• Free revisions (non-monotonic counter-offer)

• Social model (trust, friendship)

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Buyer’s acceptable setBuyer’s acceptable set

Seller’s acceptable setSeller’s acceptable set

Alternating-offer Bargaining Space: Multi-Dimensional Bargaining

00

Unit Unit priceprice

qualityquality

Feasible Feasible set set

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Buyer: I am willing to buy it for $5000 if you could replace the tires with new one.

How to direct the bargainers from being trapped into ‘no solution region’ is an important issue.

Proposed Alternating-offer Protocol

• Argumentation (persuade opponent’s belief)

• Strategic delay

• Free revision (non-monotonic)

• Range offer (instead of one point offer)

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Strategic delay & ArgumentationStrategic delay:Buyer: How much?Seller: $1000.Buyer: …Seller: $800.Buyer: hmmm….Seller: $700!Buyer: …Seller: $500!Buyer: $300.Seller: OK, $300!

Argumentation:

Buyer: How much?

Seller: $1000.

Buyer: $500?

Seller: My price is lower than others’.

Buyer: $700?

Seller: $1000 is very cheap.

Buyer: $800, OK?

Seller: OK, $800.

Free revision & Range offer Range offer:

Buyer: How much?

Seller: $1000.

Buyer: I can’t afford more than $500.

Seller: $499.

Buyer: $400, OK?

Seller: OK, $400.

Free revision:Buyer: How much?

Seller: $1000.

Buyer: $500?

Seller: 800.

Buyer: $600?

…….(Seller got a call)

Seller: $2000.

Buyer: What?

Seller: The market price increases now.

Proposed Alternating-offer Bargaining

• Bounded rationality (Simon, 1982)• Bargaining problem <X, D, 1, 2, I1, I2>• I: private information about the opponent,

world, and him/herself.• Modeling of the opponent• Belief of I.i = f(Ii) (preference may change during the

negotiation!)

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Buyer’s acceptable setBuyer’s acceptable set

Seller’s acceptable setSeller’s acceptable set

Alternating-offer Bargaining Space: Influence of Argument

00

Unit Unit priceprice

qualityquality

Feasible Feasible set set

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Use argumentation to change seller’s acceptable set (shift in seller’s private valuation)

Property of Dynamic Feasible Set in Single-Attribute Bargaining

Proposition 4. In a dynamic framework when the feasible set S moves dynamically during the bargaining process (e.g., due to changes of private valuations), then the existence of a single-attribute bargaining solution is guaranteed if agents are rational, S and S/t < convergence rate.

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Example of Buyer’s Utility Functions

BBMBt

WOB MvpU 1

SOB

SOB

AccB PMPvU

WOB

SOutB

BOB

BOB

SAccBt

COB UpPMPvpU

1

)|~()1( SOutSAccppp BSOutB

SAccB

WOB

SOutB

COB

COB

SAccBt

SDB UpPMPvpU

1

WOB

SOutBNEW

COB

COB

SAccBNEWt

ArgB UpPMPvpU

1

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Example of Seller’s Utility Functions

SSMSt

WOS vMpU

1

SBO

SBOAcc

S MPvPU

WOS

BOutSS

SOS

SOBAccSt

COS UPMPvPpU

1

WOS

BOutSS

COS

COBAccSt

SDS UpMPvPpU

1

WOS

BOutSNEWS

COS

COBAccSNEWt

ArgS UpMPvPpU

1

)|~()1( BOutBAccppp SBOutS

BAccS

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Next Steps

• Comparing the new bargaining protocol to the classical bargaining protocol:

• Ratio of failure

• Length of bargaining

• Computational cost

• Fairness

• Participation rate

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Conclusion

• A study on the existence of single-attribute bargaining solutions has been carried out (see the paper)

• Some critical bargaining criteria have been pointed out

• A bargaining framework with some modifications has been proposed

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THANK YOU!

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