A Secure and Fair Negotiation Protocol in Highly Complex Utility Space Based on Cone-Constraints

Multiple issue negotiation represents an important field of study. Our work focuses on negotiations with multiple interdependent issues in which agent utility functions are highly nonlinear. This paper presents the following three novel points on multiple interdependent issues negotiations. First, we define a utility function based on ``cone-constraints". This utility function is more realistic than existing works and configures the risk attitudes to the cone-constraint. If the utility function has cone-constraint features, the utility space becomes extremely nonlinear, making it very difficult to find the optimal agreement point. Second, we propose the concept of approximated fairness and the proximity to the Nash bargaining solution. Fairness represents how fairly the agreement divides the total utility per agent. The proximity to the Nash bargaining solution represents how close a contract is to the Nash bargaining solution. Third, we propose a Secure •& Fair Mediator Protocol (SFMP) with approximated fairness. SFMP can completely conceal the agent\´s private information and reach an agreement considering the fairness, the Nash bargaining solution, and social welfare. We demonstrate that SFMP is better for Nash contract and social welfare than existing work in highly nonlinear utility space. Moreover, we demonstrate that SFMP with a genetic algorithm (GA) is superior for finding multiple Pareto-optimal agreement points in a very highly complex negotiation compared with a search algorithm to find a contract that directly maximizes Nash products.