Ranking efficient DMUs using cooperative game theory

The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an ef- ficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods

Soluciones Estables en Juegos Cooperativos bajo Incertidumbre

Los juegos cooperativos con múltiples escenarios modelan situaciones de decisión bajo incertidumbre, cuando se tiene que repartir un bien entre un conjunto de individuos, teniendo en cuenta los valores de las coaliciones bajo diferentes escenarios simult ́aneamente o bajo diferentes estados de la naturaleza. En este trabajo se proponen y analizan diferentes conceptos de solución para este tipo de juegos y se proporcionan procedimientos para calcular los repartos que generan. En particular, se introducen los núcleos de ponderaci ́on como solución y se analizan las relaciones entre ́estos y los conceptos existentes en la literatura: núcleo de preferencia y núcleo de dominancia. A continuación, se considera la posibilidad de incorporar informaci ́on parcial sobre las probabilidades de ocurrencia de los distintos escenarios con objeto de obtener conjuntos de repartos que sean estables cuando se dispone de información probabilística. Para ello se presentan nuevos conceptos de núcleo con información parcial que extienden las nociones de núcleo de preferencia y núcleo de dominancia. Se investigan las relaciones entre ellos y se proporciona el procedimiento para el c ́alculo de los resultados que generan.Multiple scenario cooperative games model situations where the worth of the coalitions is valued in several scenarios simultaneously or under different states of nature. We focus on the identification of those allocations which are stable in the sense that agents have no incentives to abandon the group. The stability of an allocation depends on how the quantities the coalitions obtain are compared with the vector-valued worth of the coalition, therefore, different extensions of the notion of core emerge, depending on how these comparisons are made. We introduce the new notions of weighting cores and analize the relationships between them and the existing core solutions. We also address the inclusion in the model of partial information about the probabilities of occurrence of the scenarios. In order to identify allocations which are also stable in the presence of probability information, we extend the notions of core to this new setting, and provide results which permit the efective calculation of the corresponding sets of allocations

Medición de la eficiencia laboral en Andalucía (España): una aproximación DEA

This paper analyses the labour efficiency in Andalusia, and takes into account labour and demographic characteristics of the Andalusian municipalities. Data Envelopment Analysis (DEA) is the methodology employed. The results obtained indicate differences at the municipal level that depend on the geographical arrangement, with the provincial capitals being the least efficient. An inverse relationship is established between the size of the municipality (in terms of number of inhabitants) and its labour efficiency: the smaller the size of the municipality, the greater the efficiency. The distance to the capital is also important in establishing the efficiency: the greater the distance to the capital, the greater the efficiency.Este trabajo analiza la eficiencia laboral en Andalucía, atendiendo a características laborales y demográficas de los municipios andaluces. La metodología empleada para obtener las mediciones de eficiencia es el Análisis Envolvente de Datos (DEA). Los resultados obtenidos indican diferencias a nivel municipal dependiendo de la disposición geográfica, siendo las capitales de provincia las menos eficientes. Se establece una relación inversa entre el tamaño del municipio (en términos del número de habitantes) y su eficiencia laboral: cuanto menor es el tamaño del municipio, mayor es la eficiencia. La distancia a la capital también es importante para establecer la eficiencia: cuanto mayor es la distancia a la capital, mayor es la eficiencia

Efficiency analysis on the consumption of software piracy in OECD countries

This paper focuses on one of the topics of copyright economics: the study of software piracy and its determinants. The efficiency of OECD countries regarding the consumption of illegal software is analyzed. In this vein, efficiency is associated with the minimal consumption of software piracy according to the socioeconomic characteristics of a nation. Data Envelopment Analysis is the methodology employed, which assigns an efficiency score to the countries in order to establish a ranking of efficiency. Additionally, a relationship is established between the legal origin of the copyright law of a country and its efficiency level. The results of the efficiency analysis show that the efficient countries are Austria, Hungary, Japan, Korea, Mexico and Slovakia; this leads to the affirmation that the countries with lower levels of piracy are not always efficient. According to the legal origin of copyright law, countries with a German origin are the most efficient. Consequently, the efficiency score is not related to the level of software piracy but to the legal origin.Ministerio de Ciencia, Innovación y Universidades PGC2018- 095786-B-I0

Soluciones Estables en Juegos Cooperativos bajo Incertidumbre.

Multiple scenario cooperative games model situations where the worth of the coalitions is valued in several scenarios simultaneously or under di erent states of nature. We focus on the identification of those allocations which are stable in the sense that agents have no incentives to abandon the group. The stability of an allocation depends on how the quantities the coalitions obtain are compared with the vector-valued worth of the coalition, therefore, diferent extensions of the notion of core emerge, depending on how these comparisons are made. We introduce the new notions of weighting cores and analize the relationships between them and the existing core solutions. We also address the inclusion in the model of partial information about the probabilities of occurrence of the scenarios. In order to identify allocations which are also stable in the presence of probability information, we extend the notions of core to this new setting, and provide results which permit the efective calculation of the corresponding sets of allocations.Los juegos cooperativos con múltiples escenarios modelan situaciones de decisión bajo incertidumbre, cuando se tiene que repartir un bien entre un conjunto de individuos, teniendo en cuenta los valores de las coaliciones bajo diferentes escenarios simultáneamente o bajo diferentes estados de la naturaleza. En este trabajo se proponen y analizan diferentes conceptos de solución para este tipo de juegos y se proporcionan procedimientos para calcular los repartos que generan. En particular, se introducen los núcleos de ponderación como solución y se analizan las relaciones entre éstos y los conceptos existentes en la literatura: núcleo de preferencia y núcleo de dominancia. A continuación, se considera la posibilidad de incorporar información parcial sobre las probabilidades de ocurrencia de los distintos escenarios con objeto de obtener conjuntos de repartos que sean estables cuando se dispone de información probabilitica. Para ello se presentan nuevos conceptos de núcleo con información parcial que extienden las nociones de nucleo de preferencia y nucleo de dominancia. Se investigan las relaciones entre ellos y se proporciona el procedimiento para el cálculo de los resultados que generan