Production-inventory games and pmas games: characterizations of the Owen point

TL;DR

The paper addresses the Owen point in production-inventory (PI) games and clarifies its relation to PMAS-games and concave games. It proves that PI-games coincide with PMAS-games, showing the Owen point is a core-allocation realizable via population-monotonic allocation schemes, and it provides three distinct axiomatic characterizations of the Owen point, including a full eight-axiom framework and reduced versions under inessentiality, plus a PMAS-consistency approach. These contributions connect PI-cooperation with non-negative cost games equipped with pmasses and establish structural guidance for fair, monotone cost-sharing in finite-horizon production-inventory coordination. The results have practical significance for designing principled allocation rules in supply chains where production, inventory, and backlog costs are shared among cooperating firms.

Abstract

Production-inventory games were introduced in Guardiola et al. (2007) as a new class of totally balanced combinatorial optimization games. From among all core-allocations, the Owen point was proposed as a specifically appealing solution. In this paper we study some relationships of the class of production-inventory games and other classes of new and known games. In addition, we propose three axiomatic characterizations of the Owen point. We use eight axioms for these characterizations, among those, inessentiality and additivity of players' demands are used for the first time in this paper.

Theorems & Definitions (15)

• Proposition 3.1
• Theorem 3.2
• Corollary 3.3
• Example 4.1
• Proposition 4.2
• Proposition 4.3
• Theorem 4.4
• Remark 4.5
• Remark 4.6
• Example 4.7