an extended alternating-offers bargaining protocol for automated negotiation in multi-agent systems...
Post on 14-Jan-2016
222 Views
Preview:
TRANSCRIPT
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
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
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)
buyer’s buyer’s private private valuationvaluation
Unit Unit priceprice
qualityquality
Feasible Feasible set set
possible solutions here
No solution here
CoopIS-02, Irvine, CA
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
CoopIS-02, Irvine, CA
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)
CoopIS-02, Irvine, CA
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
CoopIS-02, Irvine, CA
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)
CoopIS-02, Irvine, CA
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!)
CoopIS-02, Irvine, CA
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
CoopIS-02, Irvine, CA
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
CoopIS-02, Irvine, CA
THANK YOU!
CoopIS-02, Irvine, CA
top related