Finding Nash bargaining solutions for multi-issue negotiations: a preliminary result

  • Authors:

  • Katsuhide Fujita;Takayuki Ito;Mark Klein

  • Affiliations:

  • Nagoya Institute of technology, Gokiso-cho Showa-ku, Nagoya-shi Aichi-ken, Japan;Nagoya Institute of technology/ Massachusetts Institute of Technology, Gokiso-cho Showa-ku, Nagoya-shi Aichi-ken, Japan;Massachusetts Institute of Technology, Cambridge

  • Venue:
  • HuCom '08 Proceedings of the 1st International Working Conference on Human Factors and Computational Models in Negotiation
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

Abstract

We envision the future in which large number of participants collaborate, negotiate, and reach consensus through computer supported negotiation support system against a global problem in the world. Multi interdependent issues negotiation has been studied widely since such most real-world negotiation involves multiple interdependent issues. Our work focuses on negotiation with multiple interdependent issues, in which agent utility functions are nonlinear. Existing works have not yet concerned with agents' private information that should be concealed from others in negotiations. In this paper, we propose Distributed Mediator Protocol (DMP) to securely find the agreements that satisfy the Pareto optimality. DMP successfully conceals agents' private information. Then, we propose the following two measures for selecting the final agreements from the set of Pareto-optimal contracts. First, we propose "approximated fairness," which represents how fair the contract is for each agent. We employ deviation for measuring the difference of utilities achieved by agents. Second, we propose the rate of Nash bargaining solution, which represents how close the contract is to the Nash bargaining solution. The Nash bargaining solution maximizes the product of each agent's utilities (Nash product) in our model. The approximated fairness helps the mediator find the contract that is close to the Nash bargaining solution. This is because the Nash product will be increased if approximated fairness becomes small. Moreover, we compare DMP with a search algorithm (called Direct Search) to find a contract which maximizes Nash products directly. Direct Search is usually better for finding the Nash bargaining solution. However, Direct Search isn't always better from the Pareto Optimality and Fairness if the situation is difficult for finding the Nash bargaining solution. We compare DMP with Direct Search from Nash product and Pareto optimality in the experiments.