Core Nonemptiness of Stratified Pooling Games: A Structured Markov Decision Process Approach

Abstract

We study several service providers that keep spare parts in stock to protect for downtime of their high-tech machines and that face different downtime costs per stockout. Service providers can cooperate by forming a joint spare parts pool, and we study the allocation of the joint costs to the individual service providers by studying an associated cooperative game. In extant literature, the joint spare parts pool is typically controlled by a suboptimal full-pooling policy. A full-pooling policy may lead to an empty core of the associated cooperative game, and we show this result in our setting as well. We then focus on situations where service providers apply an optimal policy: a stratification that determines, depending on the real-time on-hand inventory, which service providers may take parts from the pool. We formulate the associated stratified pooling game by defining each coalitional value in terms of the minimal long-run average costs of a Markov decision process. We present a proof demonstrating that stratified pooling games always have a nonempty core. This five-step proof is of interest in itself, because it may be more generally applicable for other cooperative games where coalitional values can be defined in terms of Markov decision processes.

Research on Civil Aircraft Spare Parts Pooling Evolutionary Game based on Supervision and Incentive Mechanism

“…The expected profit when airline B adopts an uncooperative strategy, B U ′′ , as shown in (6). The average profit of airline B, B U , as shown in (7).…”

“…At present, most scholars' research on SPPA mainly focuses on the allocation of resource for spare parts pooling [4], spare parts supply chain management [5], cooperation revenue allocation game [6], and cooperation cost allocation game [7]. However, additional research is needed on strategies to promote multi-airline game players to reach alliances.…”

Stable allocations for choice-based collaborative price setting

“…Cooperative game theory was successfully applied to various types of real-life collaborative settings. For instance, it has been used to identify fair prices for vaccine exchange between countries in times of pandemics ( Westerink-Duijzer, Schlicher, & Musegaas, 2020 ), to help museums to decide how to share the profits arising from a museum pass ( Ginsburgh & Zang, 2003 ), to identify fair prices to share railway equipment amongst railway contractors ( Schlicher, Slikker, & van Houtum, 2017;Schlicher, Slikker, & van Houtum, 2018;Schlicher, Slikker, van Jaarsveld, & van Houtum, 2020 ), and to help service operations in factories to divide cost savings when they decide to optimally re-balance their production lines ( Anily & Haviv, 2017 ).…”

Anonymity in sharing the revenues from broadcasting sports leagues

“…Other well known instances to which the literature has paid attention are: airport problems (e.g., Littlechild and Owen, 1973), bankruptcy problems (e.g., O'Neill, 1982;Thomson, 2019a), telecommunications problems (e.g., van den Nouweland et al, 1996), minimum cost spanning tree problems (e.g., Bergantiños and Vidal-Puga, 2021), transport problems (e.g., Algaba et al 2019;Estañ et al 2021), inventory problems (e.g., Guardiola et al, 2021), liability problems with rooted tree networks (e.g. Oishi et al, 2023), knapsack problems (e.g., Arribillaga and Bergantiños 2023), pooling games (Schlicher et al 2020), m-attribute games (Özen et al, 2022), urban consolidation centers (Hezarkhani et al, 2019), and scheduling problems with delays (Gonçalves-Dosantos et al, 2020) .…”