An Extended Alternating- An Extended Alternating- Offers Bargaining Protocol Offers Bargaining Protocol for Automated Negotiation for Automated Negotiation in Multi-agent Systems in Multi-agent Systems P. Winoto, G. McCalla & J. Vassileva Department of Computer Science University of Saskatchewan Presented by Julita Vassileva CoopIS-02, Irvine, CA
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An Extended Alternating-Offers Bargaining Protocol for Automated Negotiation in Multi-agent Systems P. Winoto, G. McCalla & J. Vassileva Department of.
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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
CoopIS-02, Irvine, CA
Automated Negotiation in Multi-agent Systems (MAS)
CoopIS-02, Irvine, CA
$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)
CoopIS-02, Irvine, CA
Auctions
Very efficient, but:
– Scheduled in advanced
– Non-negotiable
– Only for price
– Controlled by auctioneer
Alternative: Bargaining!!
CoopIS-02, Irvine, CA
Bargaining
• Axiomatic bargaining– Bargainers provide information (proposals, facts, and other
• 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
CoopIS-02, Irvine, CA
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.
CoopIS-02, Irvine, CA
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)
• 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
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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.
CoopIS-02, Irvine, CA
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
CoopIS-02, Irvine, CA
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
CoopIS-02, Irvine, CA
Next Steps
• Comparing the new bargaining protocol to the classical bargaining protocol:
• Ratio of failure
• Length of bargaining
• Computational cost
• Fairness
• Participation rate
CoopIS-02, Irvine, CA
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