The Stability of the Roommate Problem Revisited

The lack of stability in some matching problems suggests that alternative solution concepts to the core might be applied to find predictable matchings. We propose the absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts some other matchings when the core is empty. Furthermore, it satisfies an interesting property of outer stability. We also characterize the absorbing sets, determine their number and, in case of multiplicity, we find that they all share a similar structure.roommate problem, core, absorbing sets

A new solution for the roommate problem: The Q-stable matchings

The aim of this paper is to propose a new solution for the roommate problem with strict preferences. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2])and maximum stable matchings (Ta [30] [32]). We find that almost stable matchings are incompatible with the other two solutions. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which are called Q-stable matchings. These matchings are core consistent and we offer an effi cient algorithm for computing one of them. The outcome of the algorithm belongs to an absorbing set.This research is supported by the Spanish Ministry of Science and Innovation (ECO2010- 17049 and ECO2012-31346), co-funded by ERDF, by Basque Government IT-568-13 and by the Government of Andalusia Project for Excellence in Research (P07.SEJ.02547). P eter Bir o also acknowledges the support from the Hungarian Academy of Sciences under its Momentum Programme (LD-004/2010), and the Hungarian Scientific Research Fund,OTKA, grant no.K108673

Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms

There is a wide range of economic problems that involve the exchange of indivisible goods with no monetary transfers, starting from the housing market model of the seminal paper by Shapley and Scarf (1974) to problems such as the kidney exchange or the school choice problem. The classical solution to many of these models is to apply a mechanism called Top Trading Cycles, attributed to David Gale, which satisfies good properties for the case of strict preferences. In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, which generalize the Top Trading Cycles to the general case in which individuals are allowed to report indifferences, while preserving a maximal possible set of its desirable properties.Authors acknowledge financial support from the Spanish Ministry of Education and Science, through the projects ECO2009-11213 and ECO2009-12836, from Basque Government through the project GIC07/146-IT-377-07, from Andalusian Government through the project P07.SEJ.02547 and from Belgian Federal Government through the IAP Project (contract 6/09)

The Stability of the Roommate Problem Revisited

The lack of stability in some matching problems suggests that alternative solution concepts to the core might be applied to find predictable matchings. We propose the absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts some other matchings when the core is empty. Furthermore, it satisfies an interesting property of outer stability. We also characterize the absorbing sets, determine their number and, in case of multiplicity, we find that they all share a similar structure.This research has been supported by the University of the Basque Country under project 1/UPV 00031.321-HA-7903/2000 and project GIU06/44 and by the Spanish Ministerio de Educación y Ciencia under project SEJ2006-05455, cofunded by FEDER and project BEC2000-0875. It has also benefited from the Franco-Spanish Exchange Program HF-2006-0021/EGIDE-Picasso

The effect of initial inequality on meritocracy: a voting experiment on tax redistribution

According to Alesina and Angeletos (2005), societies are less redistributive but more efficient when the median voter believes that effort and talent are much more important than luck in determining income. We test these results through a lab experiment in which participants vote over the tax rate and their pre-tax income is determined according to their performance in a real-effort task with leisure time. Subjects receive either a high or a low wage and this condition is either obtained through their talent in a tournament or randomly assigned. We compare subjects' decisions in these two different scenarios, taking into consideration different levels of wage inequality. In our framework, this initial income inequality turns out to be crucial to support the theoretical hypothesis of Alesina and Angeletos (2005). Overall, we find that, only if the wage inequality is high, subjects choose a lower level of income redistribution and provide a higher effort level in the scenario in which high-wage subjects are selected based on their talent through a tournament (than when it is randomly assigned). Thus, we confirm almost all theoretical results in Alesina and Angeletos (2005) when the wage inequality is high enough. The big exception is for efficiency (measured as the sum of total payoffs), since theoretical results are not significant for both wage inequality scenarios

Allocating the costs of cleaning a river: expected responsibility versus median responsibility

We consider the problem of cleaning a transboundary river, proposed by Ni and Wang (Games Econ Behav 60:176–186, 2007). A river is modeled as a segment divided into subsegments, each occupied by one region, from upstream to downstream. The waste is transferred from one region to the next at some rate. Since this transfer rate may be unknown, the social planner could have uncertainty over each region’s responsibility. Two natural candidates to distribute the costs in this setting would be the method that assigns to each region its expected responsibility and the one that assigns to each region its median responsibility. We show that the latter is equivalent to the Upstream Responsibility method (Alcalde-Unzu et al. in Games Econ Behav 90:134–150, 2015) and the former is a new method that we call Expected Responsibility. We compare both solutions and analyze them in terms of a new property of monotonicity.Jorge Alcalde-Unzu acknowledges the financial support from the Spanish Government through projects PGC2018-093542-B-I00 and ECO2017-91589-EXP. María Gómez-Rúa acknowledges the financial support from the Spanish Government through projects ECO2014-52616-R and ECO2017-82241-R and the Galician Government through projects GRC 2015/014 and ED431B 2019/34. Elena Molis acknowledges the financial support from the Spanish Government through projects ECO2015-67519-P and PID2019-110783GB-I00, the Basque Government through project IT-568-13 and the Andalusian Government through the projects SEJ1436 and SEJ492

Sharing the costs of cleaning a river: the Upstream Responsibility rule

The cleaning up of waste present in transboundary rivers, which requires the cooperation of different authorities, is a problematic issue, especially when responsibility for the discharge of the waste is not well-defined. Following Ni and Wang (2007) we assume that a river is a segment divided into several regions from upstream to downstream. We show that when the transfer rate of the waste is unknown, the clean-up cost vector provides useful information for estimating some limits in regard to the responsibility of each region. We propose a cost allocation rule, the Upstream Responsibility rule, which takes into account these limits in distributing costs “fairly” and we provide an axiomatic characterization of this rule via certain properties based on basic ideas concerning the responsibility of regions.Jorge Alcalde-Unzu acknowledges the financial support from the Spanish Government through the project ECO2012–34202 and Fundación Ramón Areces. María Gómez-Rúa acknowledges the financial support from the Spanish Government through the project ECO2011-23460 and the Galician Government through the project 2013XGCEDU08072013EMER. Elena Molis acknowledges the financial support from the Spanish Government through the projects ECO2012–31346 and ECO2013–44879–R, from the Consejería de Economía, Innovación, Ciencia y Empleo, Junta de Andalucía through the projects SEJ–492 and SEJ–1436 and from the Basque Government through the project IT568–13

A new solution for the roommate problem: The Q-stable matchings

The aim of this paper is to propose a new solution for the roommate problem with strict preferences. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2])and maximum stable matchings (Ta [30] [32]). We find that almost stable matchings are incompatible with the other two solutions. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which are called Q-stable matchings. These matchings are core consistent and we offer an effi cient algorithm for computing one of them. The outcome of the algorithm belongs to an absorbing set.This research is supported by the Spanish Ministry of Science and Innovation (ECO2010- 17049 and ECO2012-31346), co-funded by ERDF, by Basque Government IT-568-13 and by the Government of Andalusia Project for Excellence in Research (P07.SEJ.02547). P eter Bir o also acknowledges the support from the Hungarian Academy of Sciences under its Momentum Programme (LD-004/2010), and the Hungarian Scientific Research Fund,OTKA, grant no.K108673