Axioms Of Efficiency Research Articles

The on-line transfer rule for queueing with arrivals

We consider the queueing problem with arrivals, or the arrival queueing problem, where agents arrive at different (time) slots to process their jobs in a service facility and each job requires the same amount of processing time which is normalized to one. Each agent has one job to process and the facility can process only one job at each slot. We introduce a rule for the arrival queueing problem, which we call the on-line transfer rule, by adapting the minimal transfer rule of the static queueing problem (Maniquet, 2003) but incorporating the time span which each agent observes. We provide axiomatic characterizations of the on-line transfer rule by imposing the axioms of efficiency, Pareto indifference, equal treatment of equals, independence of larger costs, and consistency from later-arrived-later-served agents. We also introduce and characterize an alternative rule for the arrival queueing problem which adapts the maximal transfer rule of the static queueing problem (Chun, 2006a).

Fairness and efficiency of the random serial dictatorship on preference domains with a tier structure

In this note, we study the envy-freeness and ordinal efficiency of the random serial dictatorship (RSD) rule on preference domains with a tier structure. Specifically, we obtain that the RSD rule is envy-free on restricted tier preference domains. For the ordinal efficiency axiom, we show that the almost-singleton condition is not sufficient for the RSD rule to be ordinally efficient. For assignment problems on the restricted tier preference domains, we characterize the condition under which the RSD rule is ordinally efficient.

An efficient solidarity value for interval cooperative games

This paper proposes an efficient interval solidarity value that operates well for interval cooperative games. In addition to the axioms of symmetry, efficiency, and additivity, this value also satisfies two new axioms, namely, interval-egalitarian A-null player and interval differential marginality. The interval-egalitarian A-null player axiom equally divides the result of the difference between the grand coalition value and the sum of the solidarity value of players in the degenerate interval game among A-null players. The interval differential marginality axiom is an interval version of the Casajus differential marginality axiom. This property states that the difference in the interval solidarity value of two players is determined by the difference between their average marginal contributions in the degenerate interval game. Eventually, the efficiency results and applicability of the proposed approach are compared with those of the other methods.

Axiomatizations of convex compromise rules for redistribution of non-negative income

We adopt an axiomatic approach to explore the redistribution rules for income redistribution problems. We formalize two axioms concerning how changes in the income of one or a pair of individuals affect others’ rewards. Together with the standard axioms of efficiency, order preservation, and non-negativity, our resulting axioms of equal benefits from additional income and pairwise reallocation invariance characterize the family of convex compromise rules. We show that the family can also be characterized by efficiency, equal benefits from additional income, nullity, and monotonicity. Strengthening equal benefits from additional income to differential invariance leads to alternative axiomatizations, where pairwise reallocation invariance is superfluous in the former.

An Axiomatization of the Value α for Games Restricted by Augmenting Systems

The value α for augmenting structures was introduced and axiomatically characterized by Algaba, Bilbao and Slikker. In this paper, we provide a new axiomatization of the value α for augmenting structures by using marginality for augmenting structures and the standard axioms of component efficiency, equal treatment of necessary players and loop-null.

Efficiency, equity, and social rationality under uncertainty

In a simple model where agents’ monetary payoffs are uncertain, this paper examines the aggregation of subjective expected utility functions which are interpersonally noncomparable. A maximin social welfare criterion is derived from axioms of efficiency, ex post equity, and social rationality, combined with the independence of beliefs and risk preferences in riskless situations (Chambers and Echenique in Games Econ Behav 76:582–595, 2012). The criterion compares allocations by the values of the prospects composed of the statewise minimum payoffs evaluated by the certainty equivalents. Because of this construction, the criterion is egalitarian and risk averse.

Axiomatizations of the $$\beta $$ and the score measures in networks

Monotonicity is an appealing principle of relational power measures in social networks. It states that as the influence of an individual changes, the relational power measure should change in the same direction. We axiomatically characterize the $$\beta $$ - and score-measures on directed networks using three axioms: two different monotonicity axioms, the same symmetry axiom and two different efficiency axioms, respectively. For every individual, the $$\beta $$ -measure refers to a weighted sum over all dominated individuals by itself, in which for each dominated individual the weight is given by the reciprocal of the number of its dominators, while the score-measure refers simply to the number of dominated individuals by itself. We also extend the result for the score-measure to undirected networks.

Cooperative games on simplicial complexes

In this work, we define cooperative games on simplicial complexes, generalizing the study of probabilistic values of Weber (1988) and quasi-probabilistic values of Bilbao et al. (2001). Applications to Multi-Touch Attribution and the interpretability of the Machine-Learning prediction models motivate these new developments (Lundberg and Lee, 2017; Ribeiro et al., 2016; Strumbelj and Kononenko, 2013; Shrikumar et al., 2017; Datta et al., 2016; Bach et al., 2015).We deal with the axiomatization provided by the λi-dummy and the monotonicity requirements together with a probabilistic form of the symmetric and the efficiency axioms. We also characterize combinatorially the set of probabilistic participation influences as the facet polytope of the simplicial complex.

Axiomatic characterizations of the egalitarian solidarity values

We define and characterize the class of all egalitarian solidarity values, which are convex combinations of the solidarity value and the equal division solution. First, assuming that the parameter is given exogenously, we provide two alternative characterizations of the corresponding value: Either with the classical axioms of efficiency, additivity and symmetry,and a new axiom called α-egalitarian A-null player axiom; or replacing the additivity and theα-egalitarian A-null playeraxioms by a new axiom called α-average marginality. Finally, we give two characterizations of the whole family of egalitarian solidarity values in such a way that the parameter α is obtained endogenously by the set of axioms.

Fair social orderings for the sharing of international rivers: A leximin based approach

We consider the problem of sharing water among agents located along a river. A vector of entitlements specifies the amount of water each agent is entitled to. A social welfare function provides a complete ranking of the allocations based on the vector of r-equivalents. The r-equivalent of an agent at an allocation is the amount of money that, when consumed with the agent's entitlement, leaves the agent indifferent to its bundle assigned by the allocation. Using axioms of efficiency and fairness, a social welfare function called the r-leximin is characterized. The r-leximin ranks an allocation over another if the vector of r-equivalents of the former leximin dominates the vector of r-equivalents of the latter. We further show that maximizing the r-leximin over the set of acceptable allocations (defined in the sense of the core) leads to a class of solutions that meet the three key objectives of international river management: efficiency, fairness, and stability. We show that this class contains new solutions as well as the downstream incremental solution of Ambec and Sprumont (2002). Finally, we present an application of our approach to the case of the Blue Nile River Basin, shared among Ethiopia, Sudan and Egypt. JEL Codes D62, C71.

Development of a highly efficient Axiom\u2122 70 K SNP array for Pyrus and evaluation for high-density mapping and germplasm characterization

BackgroundBoth a source of diversity and the development of genomic tools, such as reference genomes and molecular markers, are equally important to enable faster progress in plant breeding. Pear (Pyrus spp.) lags far behind other fruit and nut crops in terms of employment of available genetic resources for new cultivar development. To address this gap, we designed a high-density, high-efficiency and robust single nucleotide polymorphism (SNP) array for pear, with the main objectives of conducting genetic diversity and genome-wide association studies.ResultsBy applying a two-step design process, which consisted of the construction of a first ‘draft’ array for the screening of a small subset of samples, we were able to identify the most robust and informative SNPs to include in the Applied Biosystems™ Axiom™ Pear 70 K Genotyping Array, currently the densest SNP array for pear. Preliminary evaluation of this 70 K array in 1416 diverse pear accessions from the USDA National Clonal Germplasm Repository (NCGR) in Corvallis, OR identified 66,616 SNPs (93% of all the tiled SNPs) as high quality and polymorphic (PolyHighResolution). We further used the Axiom Pear 70 K Genotyping Array to construct high-density linkage maps in a bi-parental population, and to make a direct comparison with available genotyping-by-sequencing (GBS) data, which suggested that the SNP array is a more robust method of screening for SNPs than restriction enzyme reduced representation sequence-based genotyping.ConclusionsThe Axiom Pear 70 K Genotyping Array, with its high efficiency in a widely diverse panel of Pyrus species and cultivars, represents a valuable resource for a multitude of molecular studies in pear. The characterization of the USDA-NCGR collection with this array will provide important information for pear geneticists and breeders, as well as for the optimization of conservation strategies for Pyrus.

Coalitional surplus desirability and the equal surplus division value

In this paper, we propose axiomatic results with two variations of the recent coalitional desirability axiom (Beal et al., 2019), respectively named as coalitional surplus desirability and average coalitional surplus desirability. Particularly, we show that while the first variation is incompatible with the well-known efficiency axiom, the second variation is characteristic for the equal surplus division value, together with the well-known efficiency and additivity axioms.

Effects of Players’ Nullification and Equal (Surplus) Division Values

We provide axiomatic characterizations of the solutions of transferable utility (TU) games on the fixed player set, where at least three players exist. We introduce two axioms on players’ nullification. One axiom requires that the difference between the effect of a player’s nullification on the nullified player and on the others is relatively constant if all but one players are null players. Another axiom requires that a player’s nullification affects equally all of the other players. These two axioms characterize the set of all affine combinations of the equal surplus division and equal division values, together with the two basic axioms of efficiency and null game. By replacing the first axiom on players’ nullification with appropriate monotonicity axioms, we narrow down the solutions to the set of all convex combinations of the two values, or to each of the two values.

Asymptotic properties of welfare relations

We introduce and discuss notions of efficiency in the aggregation of infinite utility streams. For any utility streams x and y, our efficiency criteria roughly require this: If a utility stream x dominates another utility stream y and if the asymptotic density of the set of coordinates in favor of x is strictly positive, then x is socially preferred to y. As a robustness check of the proposed efficiency axioms we explore the consistency of the axioms with notions of equity. Our main results characterize one period utility domains, i.e., the set of utilities Y attainable by each generation, admitting a social welfare aggregator with the desired properties.

Egalitarianism with a dash of fair efficiency

We study the construction of Paretian egalitarian social ordering functions in a distribution model with multiple goods and heterogeneous preferences. Given the impossibility to combine equality of resources with efficiency (Fleurbaey and Trannoy, Soc Choice Welf 21:243–263, 2003), we define weaker axioms of equality and efficiency relying on the mean bundle in the allocation. We identify a leximin social ordering function that satisfy these weaker axioms by relying on welfare measures representing the fraction of the mean bundle that would leave an agent indifferent with her bundle.

A new axiomatization of the Shapley–solidarity value for games with a coalition structure

In this paper, we propose a new kind of players as a compromise between the null player and the A-null player. It turns out that the axiom requiring this kind of players to get zero-payoff together with the well-known axioms of efficiency, additivity, coalitional symmetry, and intra-coalitional symmetry characterize the Shapley–solidarity value. This way, the difference between the Shapely–solidarity value and the Owen value is pinpointed to just one axiom.

GAINS FROM TRADE

In a social choice context, we ask whether there exists a rule in which nobody loses under trade liberalization. We consider a resource allocation problem in which the traded commodities vary. We propose an axiom stating that enlarging the set of tradable commodities hurts nobody. We show that if a rule satisfies this axiom, together with an allocative efficiency axiom and an institutional constraint axiom stating that only preferences over tradable commodities matter, gains from trade can be given to only one individual in the first step of liberalization.

Egalitarianism with a Dash of Fair Efficiency

We study the construction of Paretian egalitarian social ordering functions in a distribution model with multiple goods and heterogeneous preferences. Given the impossibility to combine equality of resources with efficiency (Fleurbaey and Trannoy, Soc Choice Welf 21:243–263, 2003), we define weaker axioms of equality and efficiency relying on the mean bundle in the allocation. We identify a leximin social ordering function that satisfy these weaker axioms by relying on welfare measures representing the fraction of the mean bundle that would leave an agent indifferent with her bundle.

A simple family of solutions for forest games

In this paper we study TU-games where the cooperation structure among the players is modeled by a forest. Using the classical component efficiency axiom and a generalized version of the component fairness axiom we obtain a family of solutions. We show that every solution in this family is based on a process of transfers among the players, and the average tree solution belongs to the family. Finally, we obtain a solution based on the degree of the nodes and we study a set of properties satisfied by this family.

On characterizations of the probabilistic serial mechanism involving incentive and invariance properties

This paper studies the problem of assigning n indivisible objects to n agents when each agent consumes one object and monetary transfers are not allowed. Bogomolnaia and Moulin (2001) proved that for n=3, the probabilistic serial mechanism is characterized by the three axioms of ordinal efficiency, envy-freeness, and weak strategy-proofness. We show that this characterization does not extend to problems of arbitrary size; in particular, it does not hold for any n≥5. A number of general characterizations of the probabilistic serial mechanism have been obtained in the recent literature by replacing weak strategy-proofness with various invariance axioms while retaining ordinal efficiency and envy-freeness. We show that weak strategy-proofness is in fact logically independent of all invariance axioms used in these characterizations.