Bi-objective optimization problems with two decision makers: refining Pareto-optimal front for equilibrium solution

Mohammadali S. Monfared (), Sayyed Ehsan Monabbati () and Mahsa Mahdipour Azar ()
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Mohammadali S. Monfared: Alzahra University
Sayyed Ehsan Monabbati: Alzahra University
Mahsa Mahdipour Azar: Alzahra University

OR Spectrum: Quantitative Approaches in Management, 2020, vol. 42, issue 2, No 8, 567-584

Abstract: Abstract The Pareto-optimality concept in multi-objective optimization theory is different from the Nash equilibrium concept in noncooperative game theory. When the objective holders are independent decision makers, i.e., human entities or organizations, any solution on the Pareto-optimal front is not necessarily an equilibrium point, hence not a valid solution. The solution has to be a Pareto-optimal-equilibrium (POE) point. In this paper, we convert a bi-objective optimization problem into a two-player game problem by introducing “induced games,” and we propose a new refinement method to find a POE point. We prove that at least one such POE point exists for a class of linear bi-objective optimization problems, and we develop an algorithm to find it. We discuss that the innovative approach considered in this paper is of real future interest to some industrial and social applications. One such example is also presented.

Keywords: Game theory; Bi-objective optimization; Nash equilibrium; Bi-matrix games; Pareto-optimal equilibrium (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00291-020-00587-9

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