An Extended Alternating-Offers Bargaining Protocol for Automated Negotiation in Multi-agent Systems P. Winoto, G. Mc. Calla & J. Vassileva Department of Computer Science University of Saskatchewan Presented by Julita Vassileva Coop. IS-02, Irvine, CA
Automated Negotiation in Multi-agent Systems (MAS) $100 $1 • Conflict of interest • Cooperative behavior in competitive situation • Applications: distributed problem solving, resource allocation, e-commerce My agent will negotiate with you Coop. IS-02, Irvine, CA
Classification of Negotiation Protocols: – auctions – bargaining – voting, etc. Negotiated Items: – single attribute (e. g. price) – multiple attribute (e. g. price and quality) Coop. IS-02, Irvine, CA
Auctions Very efficient, but: – Scheduled in advanced – Non-negotiable – Only for price – Controlled by auctioneer Alternative: Bargaining!! Coop. IS-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 Coop. IS-02, Irvine, CA
Alternating-offer Bargaining Scenario 1: Scenario 2: Buyer: How much? Seller: $1000. Buyer: $500? Seller: $800. Buyer: $600? Seller: $700! Buyer: OK, $700. Buyer: How much? Seller: $1000. Buyer: $10. Seller hangs up the phone. Coop. IS-02, Irvine, CA
Alternating-offer Bargaining Space: an Example Unit price (Seller indifferent between two point in this line) Coop. IS-02, Irvine, CA Seller’s acceptable set Feasible set seller’s private valuation buyer’s private valuation Seller’s proposal start from here possible solutions here No solution here Buyer’s acceptable set 0 proposal start from here quality
Alternating-offer Bargaining • Bargaining problem: <X, D, 1, 2> – X: feasible set – D: disagreement – : preference order of bargainers 1 and 2. • Goal: achieve x X • Solving method: backward induction (Gametheoretic approach) • Assumptions: – Perfect rationality – Perfect foresight Coop. IS-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 counteroffer) • Social model (trust, friendship) Coop. IS-02, Irvine, CA
Alternating-offer Bargaining Space: Multi-Dimensional Bargaining Unit price 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 Seller’ssolution region’ is an acceptable set Feasible important issue. set Buyer’s acceptable set 0 Coop. IS-02, Irvine, CA quality
Proposed Alternating-offer Protocol • • Argumentation (persuade opponent’s belief) Strategic delay Free revision (non-monotonic) Range offer (instead of one point offer) Coop. IS-02, Irvine, CA
Strategic delay & Argumentation Strategic 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 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. Range offer: Buyer: How much? Seller: $1000. Buyer: I can’t afford more than $500. Seller: $499. Buyer: $400, OK? Seller: OK, $400.
Proposed Alternating-offer Bargaining • Bounded rationality (Simon, 1982) • Bargaining problem <X, D, 1, 2, I 1, I 2> • 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!) Coop. IS-02, Irvine, CA
Alternating-offer Bargaining Space: Influence of Argument Unit Use argumentation price to change seller’s acceptable set (shift in seller’s private valuation) Seller’s acceptable set Feasible set Buyer’s acceptable set 0 Coop. IS-02, Irvine, CA quality
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. Coop. IS-02, Irvine, CA
Example of Buyer’s Utility Functions Coop. IS-02, Irvine, CA
Example of Seller’s Utility Functions Coop. IS-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 Coop. IS-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 Coop. IS-02, Irvine, CA
THANK YOU! Coop. IS-02, Irvine, CA
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