On Asymptotic Behavior of Some Nuclei of n-Person Games and the Piecewise Linearity of the Nucleolus

摘要

In a previous paper the authors developed a new class of solution concepts in n-person game theory as optimal solutions to specially constructed linear programming problems whose constraint matrices and hence optimal solutions depend on a certain parameter, c. In this paper asymptotic results are obtained for the limiting payoff configuration as c approaches infinity. It is shown that the limiting payoff configuration in general shares some properties with Schmeidler's solution concept of the nucleolus and under additional assumptions does converge to the nucleolus. By using recent results of Kohlberg, a new proof is obtained for the author's theorem of the piecewise linearity of the nucleolus as a function of the characteristic function of n-person games. (Author)