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

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  • Kristiaan Kerstens

    (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)

  • 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)

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.

Suggested Citation

  • Kristiaan Kerstens & Stefano Nasini & Rabia Nessah, 2025. "Natural divisibility bridging convex and nonconvex technologies: Bargaining-based estimation by cost and revenue functions," Post-Print hal-05369146, HAL.
    • Handle: RePEc:hal:journl:hal-05369146
    DOI: 10.1016/j.ejor.2025.07.046
    Note: View the original document on HAL open archive server: https://hal.science/hal-05369146v1
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    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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