TITLE

Nondominated equilibrium solutions of a multiobjective two-person nonzero-sum game in extensive form and corresponding mathematical programming problem

AUTHOR(S)
Ichiro Nishizaki; Takuma Notsu
PUB. DATE
October 2008
SOURCE
Journal of Global Optimization;Oct2008, Vol. 42 Issue 2, p201
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Abstract  In most of studies on multiobjective noncooperative games, games are represented in normal form and a solution concept of Pareto equilibrium solutions which is an extension of Nash equilibrium solutions has been focused on. However, for analyzing economic situations and modeling real world applications, we often see cases where the extensive form representation of games is more appropriate than the normal form representation. In this paper, in a multiobjective two-person nonzero-sum game in extensive form, we employ the sequence form of strategy representation to define a nondominated equilibrium solution which is an extension of a Pareto equilibrium solution, and provide a necessary and sufficient condition that a pair of realization plans, which are strategies of players in sequence form, is a nondominated equilibrium solution. Using the necessary and sufficient condition, we formulate a mathematical programming problem yielding nondominated equilibrium solutions. Finally, giving a numerical example, we demonstrate that nondominated equilibrium solutions can be obtained by solving the formulated mathematical programming problem.
ACCESSION #
34205022

 

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