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THE MAGIC OF NASH SOCIAL WELFARE IN OPTIMIZATION: DO NOT SUM, JUST MULTIPLY!

Part of: Game theory Operations research and management science

Published online by Cambridge University Press:  07 July 2022

HADI CHARKHGARD Open the ORCID record for HADI CHARKHGARD [Opens in a new window] ,
KIMIA KESHANIAN Open the ORCID record for KIMIA KESHANIAN [Opens in a new window] ,
RASUL ESMAEILBEIGI Open the ORCID record for RASUL ESMAEILBEIGI [Opens in a new window]  and
PARISA CHARKHGARD Open the ORCID record for PARISA CHARKHGARD [Opens in a new window]
HADI CHARKHGARD*
Affiliation:
Department of Industrial and Management Systems Engineering, University of South Florida, Tampa, FL33620, USA
KIMIA KESHANIAN
Affiliation:
Information and Technology Management Department, University of Tampa, Tampa, FL33606, USA; e-mail: [email protected]
RASUL ESMAEILBEIGI
Affiliation:
School of Information Technology, Deakin University, Geelong, Victoria3220, Australia; e-mail: [email protected]
PARISA CHARKHGARD
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, New South Wales2308, Australia; e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

We explain some key challenges when dealing with a single- or multi-objective optimization problem in practice. To overcome these challenges, we present a mathematical program that optimizes the Nash social welfare function. We refer to this mathematical program as the Nash social welfare program (NSWP). An interesting property of the NSWP is that it can be constructed for any single- or multi-objective optimization problem. We show that solving the NSWP could result in more desirable solutions in practice than its single- or multi-objective counterpart. We also discuss several promising approaches that could be employed to solve the NSWP in practice.

Keywords

Nash social welfareequitysingle-objective optimizationmulti-objective optimizationmultiplicative program

MSC classification

Primary: 90C29: Multi-objective and goal programming
Secondary: 90B50: Management decision making, including multiple objectives 91A12: Cooperative games
Type
Research Article
Information
The ANZIAM Journal , Volume 64 , Issue 2 , April 2022 , pp. 119 - 134
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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