A common framework to characterize the proportional rule and the average-of-awards rule in claims problems

M. Á. Mirás Calvo, M. E. Sánchez Rodríguez, J. J. Vidal Puga

For a claims problem, the proportional rule (PRO) makes awards proportional to claims while the average-of-awards rule (AA) selects the expected value of the uniform distribution over the set of awards vectors. Our goal is to establish some connections between these two division rules. We begin by defining, for each problem, the greedy coefficients that quantify the relative impact that an agent leaving the problem, after being fully compensated, has on the other claimants' awards. A rule satisfies greedy coefficient invariance if these coefficients are equal for all the claimants. The PRO and AA rules satisfy this property while other standard rules violate it. We characterize the PRO and AA rules in terms of this new axiom. First, we analyze how the PRO and AA rule behave for two-claimant problems and for valley problems (those in which al most one agent claims strictly less than the endowment). Then, we use greedy coefficient invariance to address arbitrary claims problems.

Palabras clave: claims problems, proportional rule, average-of-awards rule, axiomatic characterization

GT Teoría de Juegos IV: aplicaciones
4 de septiembre de 2026  11:10
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