Title: Multi-objective optimisation for solving cooperative continuous static games using Karush-Kuhn-Tucker conditions

Authors: Hamiden Abd El-Wahed Khalifa; Pavan Kumar

Addresses: Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia; Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt ' School of Applied Science and Languages, Mathematics Department, VIT Bhopal University, Sehore District, MP, 466114, India

Abstract: This paper introduces cooperative continuous static games (CCSG) with parameters in the cost functions of the players and in the right-hand side of the constraints. The CCSG is converted into the corresponding multi-objective nonlinear programming problem. The resulted nonlinear programming problem is converted into the single objective nonlinear programming problem through the use of the weighted sum method. A solution method for obtaining the stability set of the second kind without differentiability for the CCSG is presented using Karush-Kuhn-Tucker conditions. A numerical example is given for the illustration.

Keywords: cooperative continuous static games; CCSG; efficient solution; weighted sum method; optimal solution; Karush-Kuhn-Tucker conditions; stability.

DOI: 10.1504/IJOR.2023.128544

International Journal of Operational Research, 2023 Vol.46 No.1, pp.133 - 147

Received: 28 Feb 2020
Accepted: 07 May 2020
Published online: 26 Jan 2023 *