A reply to Ponte et al (2016) Supply chain collaboration: Some comments on the nucleolus of the beer game

David Mueller


Purpose: The aim of the paper is to pick up the result of a previously published paper in order to deepen the discussion. We analyze the solution against the background of some well-known concepts and we introduce a newer one. In doing so we would like to inspire the further discussion of supply chain collaboration

Design/methodology/approach: Based on game theoretical knowledge we present and compare seven properties of fair profit sharing.

Findings: We show that the nucleolus is a core-solution, which does not fulfil aggregate monotonicity. In contrast the Shapley value is an aggregate monotonic solution but does not belong to the core of every cooperative game. Moreover, we present the Lorenz dominance as an additional fairness criteria.

Originality/value: We discuss the very involved procedure of establishing lexicographic orders of excess vectors for games with many players.


beer game, cooperative game theory, profit allocation, nucleolus

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DOI: https://doi.org/10.3926/jiem.2430

Licencia de Creative Commons 

This work is licensed under a Creative Commons Attribution 4.0 International License

Journal of Industrial Engineering and Management, 2008-2024

Online ISSN: 2013-0953; Print ISSN: 2013-8423; Online DL: B-28744-2008

Publisher: OmniaScience