Data envelopment analysis fixed cost allocation based on dynamic bargaining game and the Nash equilibrium

Abstract

Fixed cost allocation (FCA) poses a significant challenge for decision-making units (DMUs) contributing to a shared cost. Each DMU aims to allocate the minimum possible cost to itself. As a result, different DMUs hold varying and often conflicting allocation proposals and preferences, which prevents them from reaching a consensus on the FCA outcome. This paper develops a dynamic bargaining game-based fixed cost allocation (DBG-FCA) approach within the data envelopment analysis (DEA) framework to address this issue. The DBG-FCA approach employs an iterative process where each DMU proposes its preferred allocation during each iteration. All DMUs gradually converge on a consensus FCA outcome through dynamic negotiations and gradual compromise. Notably, this consensus upholds the individual rationality of each DMU, allowing them to align their proposals with their specific interests. Furthermore, the analysis establishes that the resulting FCA solution constitutes a Nash equilibrium, guaranteeing stability and universal acceptance among the DMUs. The effectiveness of the proposed approach is further illustrated through a numerical example and a case study involving FCA across 14 bank branches, along with a comparison to existing FCA methods.