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

Kristiaan Kerstens, Stefano Nasini and Rabia Nessah

European Journal of Operational Research, 2026, vol. 329, issue 3, 966-980

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 bargaining (search for similar items in EconPapers)
JEL-codes: C78 D24 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:329:y:2026:i:3:p:966-980

DOI: 10.1016/j.ejor.2025.07.046

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