Abstract
We consider an environment in which several independent service providers can collaborate by pooling their critical, low-utilization resources that are subject to unavailability. We examine the allocation of the joint profit for such a pooled situation by studying an associated cooperative game. For this game, we will prove non-emptiness of the core, present a population monotonic allocation scheme and show convexity under some conditions. Moreover, four allocation rules will be introduced and we will investigate whether they satisfy monotonicity to availability, monotonicity to profit, situation symmetry and game symmetry. Finally, we will also investigate whether the payoff vectors resulting from those allocation rules are members of the core.
Highlights
In this paper, we will investigate situations in which several independent service providers keep the same type of critical, low-utilization resources that are subject to unavailability
We formulated a stylized model of reality in which several independent service providers can collaborate by pooling their critical, low-utilization resources that are subject to unavailability
We examined the allocation of the joint profit for such a pooled situation by studying an associated cooperative game
Summary
We will investigate situations in which several independent service providers keep the same type of critical, low-utilization resources that are subject to unavailability. Linear profit functions fit well for situations with highly profitable machines for which downtime costs increase proportional to the unavailability of the machines Under these four assumptions, the model relies on two components only: the long-run fraction of time that at least one resource is available and the profit functions of the service providers. We will introduce a cooperative game in order to examine the allocation of the additional profit for such a pooled situation. Bachrach et al (2011, 2012, 2013) introduced and investigated a new class of operations research games, called cooperative reliability games, which comes closer to our work Those games consider a directed network with one sink and one source, where each link is controlled by a self-interested agent.
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