Natural divisibility bridging convex and nonconvex technologies: Bargaining-based estimation by cost and revenue functions

Kristiaan Kerstens, Stefano Nasini and Rabia Nessah
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Stefano Nasini: LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique
Rabia Nessah: LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique

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Abstract: This contribution introduces a game-theoretic framework to infer divisibility levels from observed input–output production data. This is accomplished through a new class of M-parametrized deterministic, nonparametric technologies, which extend the conventional convex (M = ) and nonconvex (M = 1) alternatives by incorporating the new notion of natural divisibility. The statistical estimation of M is rooted in a bargaining game involving two hypothetical players pursuing conflicting objectives: efficiency and divisibility, where efficiency is measured in terms of cost and revenue functions (whose value is influenced by M, whereas the divisibility is measured by M itself. We employ the Kalai–Smorodinsky bargaining solution as an axiomatic approach to achieve an equilibrium divisibility level within the M-parametrized production possibility set. We conduct numerical tests using two secondary data sources, which reveal that M = 2 is the recurrent equilibrium divisibility. This highlights a limitation of traditional convex and nonconvex frontier methods, which both ignore the need for an endogenous assessment of natural divisibility.

Keywords: Natural divisibility estimation; Cost function; Revenue function; Cooperative bar- gaining (search for similar items in EconPapers)
Date: 2025-08-05
Note: View the original document on HAL open archive server: https://hal.science/hal-05369146v1
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Published in European Journal of Operational Research, 2025, ⟨10.1016/j.ejor.2025.07.046⟩

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Journal Article: Natural divisibility bridging convex and nonconvex technologies: Bargaining-based estimation by cost and revenue functions (2026)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05369146

DOI: 10.1016/j.ejor.2025.07.046

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