On systems of quotas based on bankruptcy with a priori unions: estimating random arrival-style rules

TL;DR

This paper introduces a sampling-based estimation method for the random arrival rule in bankruptcy problems with a priori unions, analyzing its statistical properties and applying it to real-world quota allocation.

Contribution

It adapts an estimation method of the Owen value for large agent sets in bankruptcy scenarios with a priori unions, providing theoretical analysis and practical application.

Findings

Estimator has desirable statistical properties.

Performance evaluated on literature examples.

Applied to quota system in Galicia's milk market.

Abstract

This paper addresses a sampling procedure for estimating extensions of the random arrival rule to those bankruptcy situations where there exist a priori unions. It is based on simple random sampling with replacement and it adapts an estimation method of the Owen value for transferable utility games with a priori unions, especially useful when the set of involved agents is sufficiently large. We analyse the theoretical statistical properties of the resulting estimator as well as we provide some bounds for the incurred error. Its performance is evaluated on two well-studied examples in literature where this allocation rule can be exactly obtained. Finally, we apply this sampling method to provide a new quota system for the milk market in Galicia (Spain) to check the role of different territorial structures when they are taken as a priori unions. The resulting quotas estimator is also compared with two classical rules in bankruptcy literature.