The average-of-awards rule for claims problems

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGGiven a claims problem, the average-of-awards rule (AA) selects the expected value of the uniform distribution over the set of awards vectors. The AA rule is the center of gravity of the core of the coalitional game associated with a claims problem, so it corresponds to the core-center. We show that this rule satisfies a good number of properties so as to be included in the inventory of division rules. We also provide several representations of the AA rule and a procedure to compute it in terms of the parameters that define the problem.Agencia Estatal de Investigación | Ref. MTM2017-87197-C3-2-PAgencia Estatal de Investigación | Ref. PID2019-106281GB-I0

An algorithm to compute the average-of-awards rule for claims problems with an application to the allocation of CO2 emissions

The set of awards vectors for a claims problem coincides with the core of the associated coalitional game. We analyze the structure of this set by defining for each group of claimants a, so called, utopia game, whose core comprises the most advantageous imputations available for the group. We show that, given a claims problem, the imputation set of the associated coalitional game can be partitioned by the cores of the utopia games. A rule selects for each claims problem a unique allocation from the set of awards vectors. The average-of-awards rule associates to each claims problem the geometric center of the corresponding set of awards vectors. Based on the decomposition of the imputation set, we obtain an interpretation of the average-of-awards rule as a point of fairness between stable and utopia imputations and provide a backward recurrence algorithm to compute it. To illustrate our analysis, we present an application to the distribution of CO2 emissions.Agencia Estatal de Investigación | Ref. PID2019‐106281GB‐I00Agencia Estatal de Investigación | Ref. PID2021‐124030NB‐C33Xunta de Galicia | Ref. ED481A 2021/325Universidade de Vigo/CISU

Monotonicity of the core-center of the airport game

Abstract One of the main goals of this paper is to improve the understanding of the way in which the core of a specific cooperative game, the airport gam

Deviation from proportionality and Lorenz-domination for claims problems

The Lorenz order is commonly used to compare rules for claims problems. In this paper, we incorporate the average of awards rule, the mean value of the set of awards vectors for a claims problem, to the ranking of the standard rules by proving some properties that are satisfied by this rule. We define a pair of coefficients, inspired by the Gini index, aimed at measuring, for any given claims problem, the discrepancy between the awards assigned by a rule and the proportional division. We generalize the proportionality deviation indices by introducing coefficients that measure the deviation between the awards selected by any two division rules. We show how these deviation indices are related to the Lorenz order.Ministerio de Ciencia, Innovación y Universidades | Ref. MTM2017-87197-C3-2-PMinisterio de Ciencia, Innovación y Universidades | Ref. PID2019-106281GB-I00Xunta de Galicia | Ref. ED481A 2021/32

Refining the Lorenz‐ranking of rules for claims problems on restricted domains

The comparison of the central rules for claims problems, according to the Lorenz order, has been studied not only on the entire set of problems but also on some restricted domains. We provide new characterizations of the adjusted proportional rule as being Lorenz‐maximal or Lorenz‐minimal within a class of rules on the half‐domains. Using this result, we rank the adjusted proportional, the minimal overlap, and the average‐of‐awards rules by analyzing whether or not these rules satisfy progressivity and regressivity on the half‐domains. We also find that the adjusted proportional rule violates two well‐known claim monotonicity properties.Agencia Estatal de Investigación | Ref. PID2019‐106281GB‐I00Agencia Estatal de Investigación | Ref. PID2021‐124030NB‐C33Xunta de Galicia | Ref. ED481A 2021/325Universidade de Vigo/CISU

An operational toolbox for solving conflicting claims problems

A conflicting claims problem arises when a group of agents have claims over a resource that add up to more than it is available. Typical situations are the division of property among heirs, bankruptcy problems, tax distribution, or the global emissions budget. This paper introduces the R package ClaimsProblems, a toolbox for computing and comparing the central division rules introduced in the literature. The software can be used by researchers and managers interested in problems concerning the allocation of scarce resources.Agencia Estatal de Investigación | Ref. PID2019‐106281GB‐I00Agencia Estatal de Investigación | Ref. PID2021‐124030NB‐C33Xunta de Galicia | Ref. ED481A 2021/32