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Journal of Global Optimization

, Volume 42, Issue 2, pp 201–220 | Cite as

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

  • Ichiro Nishizaki
  • Takuma Notsu
Article

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.

Keywords

Nondominated equilibrium solution Multiobjective two-person nonzero-sum game in extensive form Mathematical programming problem 

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Copyright information

© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  1. 1.Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan

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