1. An Extended Alternating-Offers Bargaining Protocol for Automated Negotiation 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

2. 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

3. 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

4. Auctions Very efficient, but: –Scheduled in advanced –Non-negotiable –Only for price –Controlled by auctioneer Alternative: Bargaining!! CoopIS-02, Irvine, CA

5. 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

6. 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

7. Buyer’s acceptable set Seller’s acceptable set Alternating-offer Bargaining Space: an Example 0 seller’s private valuation (Seller indifferent between two point in this line) buyer’s private valuation Unit price quality Feasible set possible solutions here No solution here CoopIS-02, Irvine, CA Seller’s proposal start from here Buyer’s proposal start from here

8. Alternating-offer Bargaining Bargaining problem: –X: feasible set –D: disagreement –  : preference order of bargainers 1 and 2. Goal: achieve x  X Solving method: backward induction (Game- theoretic approach) Assumptions: –Perfect rationality –Perfect foresight CoopIS-02, Irvine, CA

9. 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

10. Buyer’s acceptable set Seller’s acceptable set Alternating-offer Bargaining Space: Multi-Dimensional Bargaining 0 Unit price quality Feasible 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.

11. 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

12. 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.

13. 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.

14. Proposed Alternating-offer Bargaining Bounded rationality (Simon, 1982) Bargaining problem I: private information about the opponent, world, and him/herself. Modeling of the opponent Belief of I.  i = f(I i ) (preference may change during the negotiation!) CoopIS-02, Irvine, CA

15. Buyer’s acceptable set Seller’s acceptable set Alternating-offer Bargaining Space: Influence of Argument 0 Unit price quality Feasible set CoopIS-02, Irvine, CA Use argumentation to change seller’s acceptable set (shift in seller’s private valuation)

16. 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

17. Example of Buyer’s Utility Functions CoopIS-02, Irvine, CA

18. Example of Seller’s Utility Functions CoopIS-02, Irvine, CA

19. 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

20. 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

21. THANK YOU! CoopIS-02, Irvine, CA