On systems of quotas from bankruptcy perspective: the sampling estimation of the random arrival rule

Abstract This paper addresses a sampling procedure for estimating the random arrival rule in bankruptcy situations. It is based on simple random sampling with replacement and it adapts an estimation method of the Shapley value for transferable utility games, especially useful when dealing with large-scale problems. Its performance is analysed through the establishment of theoretical statistical properties and bounds for the incurred error. Furthermore, this tool is evaluated on two well-studied examples in literature where this allocation rule can be exactly calculated. Finally, we apply this sampling method to provide a new quota for the milk market in Galicia (Spain). After the abolition of the milk European quota system in April 2015, this region represents an example where dairy farmers suffered a massive economic impact after investing heavily in modernising their farms. The resulting quota estimator is compared with two classical rules in bankruptcy literature.