Generating Pareto Solutions in a Two-Party Setting: Constraint Proposal Methods

This paper presents a class of methods, called constraint proposal methods, for generating Pareto-optimal solutions in two-party negotiations. In these methods joint tangents of the decision makers' value functions are searched by adjusting an artificial plane constraint. The problem of generating Pareto-optimal solutions decomposes into ordinary multiple criteria decision-making problems for the individual decision makers and into a coordination problem for an assisting mediator. Depending on the numerical iteration scheme used to solve the coordination problem, different constraint proposal methods are obtained. We analyze and illustrate the behaviour of some iteration schemes by numerical examples using both precise and imprecise answers from decision makers. An example of a method belonging to the class under study is the RAMONA method, that has been previously described from a practical point of view. We present the underlying theory for it by describing it as a constraint proposal method, and include some applications.negotiation analysis, Pareto optimality, joint problem solving, multiple criteria

Recent Studies on Incentive Design Problems in Game Theory and Management Science

We study a simple principal-agent game and show how the linear wage contract can be obtained by a three-phase adjustment process. The first two processes result in an incentive compatible Pareto optimal outcome and the third process takes care of the agent's individual rationality. We also discuss a negotiation process to achieve this outcome and give the wage contract an interpretation in terms of incentive equilibrium. This concept has recently been an active research topic in dynamic games and management science studies. In this paper we present a new method for computing incentive Stackelberg solutions. The method is based on solving a system of nonlinear equations by using standard iterative schemes such as fixedpoint iteration or Broyden's method. The method can be implemented in the case of incomplete information because the leader does not need to know the followers' reaction function. The use of the method is shown in two examples: in a two player quadratic case and in a duopoly model with government coordination. More general problems and convergence properties of the method are discussed