Abstract
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 collaborationDesign/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.
Highlights
Ponte, Fernández, Rosillo, Parreño and García (2016) suggested in this journal the use of cooperative game theory within supply chain management and demonstrated the application with the famous beer game
We summarize that the nucleolus (Mueller, 2018, p. 414):
As the beer game is not convex we present a newer solution concept – the Lorenz set (Hougaard, Peleg & Thorlund-Petersen, 2001; Hougaard & Smilgins, 2016)
Summary
Ponte, Fernández, Rosillo, Parreño and García (2016) suggested in this journal the use of cooperative game theory within supply chain management and demonstrated the application with the famous beer game. Several properties of a fair solution have been identified in cooperative game theory in the last decades. A single-valued solution f satisfies the dummy-player-property if for a dummy-player i yields: fi(v) = v({i}). Additivity: A single-valued solution f satisfies additivity if for any two games v, w follows (v + w) = f (v) + f (w).
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