Nash Bargaining Game Enhanced Global Malmquist Productivity Index for Cross-Productivity Index

Reza Fallahnejad (), Mohammad Reza Mozaffari, Peter Fernandes Wanke () and Yong Tan
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Reza Fallahnejad: Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad 6817816645, Iran
Mohammad Reza Mozaffari: Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz 71993-1, Iran
Peter Fernandes Wanke: COPPEAD Graduate Business School, Federal University of Rio de Janeiro, Rua Paschoal Lemme, 355, Rio de Janeiro 21941-901, Brazil
Yong Tan: School of Management, University of Bradford, Bradford BD7 1DP, UK

Games, 2024, vol. 15, issue 1, 1-21

Abstract: The Global Malmquist Productivity Index (GMPI) stands as an evolution of the Malmquist Productivity Index (MPI), emphasizing global technology to incorporate all-time versions of Decision-Making Units (DMUs). This paper introduces a novel approach, integrating the Nash Bargaining Game model with GMPI to establish a Cross-Productivity Index. Our primary objective is to develop a comprehensive framework utilizing the Nash Bargaining Game model to derive equitable common weights for different time versions of DMUs. These weights serve as a fundamental component for cross-evaluation based on GMPI, facilitating a holistic assessment of DMU performance over varying time periods. The proposed index is designed with essential properties: feasibility, non-arbitrariness concerning the base time period, technological consistency across periods, and weight uniformity for GMPI calculations between two-time versions of a unit. This research amalgamates cross-evaluation and global technology while employing geometric averages to derive a conclusive cross-productivity index. The core motivation behind this methodology is to establish a reliable and fair means of evaluating DMU performance, integrating insights from Nash Bargaining Game principles and GMPI. This paper elucidates the rationale behind merging the Nash Bargaining Game model with GMPI and outlines the objectives to provide a comprehensive Cross-Productivity Index, aiming to enhance the robustness and reliability of productivity assessments across varied time frames.

Keywords: data envelopment analysis; global Malmquist productivity index; common weights; cross-evaluation; Nash bargaining (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2024
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