Automated negotiations have been an active research topic for many years. Most of the research work on this area focuses either on the abstract and theoretical models or on the system architectures for stand-alone negotiation applications. There is little work on identifying and studying practical algorithms for automated negotiations. In this paper, two algorithms have been proposed and their innovative applications have been discussed. The first algorithm guarantees that negotiation results are Pareto optimal solutions. The second algorithm guarantees that an agreement can be agreed upon after a certain number of proposal/counterproposal exchanges. These two algorithms can be used in the two-phase model for the automated negotiation process. In addition to these algorithms, their applications in information privacy negotiation have been described. In the information privacy management domain for service industries, it is critical for service requestors to only reveal the absolute necessary private information to the service providers. Traditionally, service requestors usually give whatever private information service providers have asked for. The grave consequence is that service providers may misuse the private information provided by service requestors, even though the service providers may have promised not to reveal it. Algorithms described in this paper can facilitate the privacy negotiation process. In order to show the concept of negotiation in information privacy, credit card information has been used to illustrate the application of algorithms.