DEA and Cooperative Game Theory

Lozano, Sebastián; Hinojosa, Miguel A.; Mármol, Amparo M.; Borrero, D. V.

doi:10.1007/978-1-4899-7705-2_9

Cited by 9 publications

(9 citation statements)

References 65 publications

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“…Therefore, the proposed approach can be placed in this category. As regards cooperative games approaches in DEA that are not related to the ranking of DMUs, the reader is referred to Lozano et al (2016), where a number of TU games approaches, as well as Nash Bargaining games approaches are reviewed (see also Lozano et al (2015), and Hinojosa et al (2016)). Among the papers reviewed in Lozano et al (2015) that apply TU games and, in particular, the Shapley value, the one that is more relevant to this research is Li and Liang (2010), which proposes a cooperative game in which the players are the input and output variables and the grand coalition is the total set that includes all the inputs and outputs.…”

Section: Literature Reviewmentioning

confidence: 99%

Ranking efficient DMUs using cooperative game theory

Hinojosa

Lozano

Borrero

et al. 2017

Expert Systems with Applications

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Section: Literature Reviewmentioning

confidence: 99%

Ranking efficient DMUs using cooperative game theory

Hinojosa

Lozano

Borrero

et al. 2017

Expert Systems with Applications

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“…It provides essential concepts, methods, and models used to assess the interaction of different agents in competitive markets and solve conflicts. Hence, notions like fairness and equity when finding allocations of the total amount the grand coalition can obtain are significant [23,59,60].…”

Section: Cooperative Games In the Dea Fieldmentioning

confidence: 99%

“…Ref. [23] stated that two main types of cooperative games apply in the DEA context: bargaining and transferable utility games (TU games). Using these games, we can address several DEA problems, such as defining common weights, defining variables relevant for efficiency measurement, efficiency decomposition, and obtaining consensus between criteria to evaluate performance.…”

Section: Cooperative Games In the Dea Fieldmentioning

confidence: 99%

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Allocating Benefits Due to Shared Resources Using Shapley Value and Nucleolus in Dynamic Network Data Envelopment Analysis

Torres,

Ramos

2024

Mathematics

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Shared resources are common among supply chain partners and also occur in multiple linked stages of an internal network. The sharing of these resources impacts the organization’s profits. This study is focused on the potential benefits of resource sharing on a three-stage network system and on the profit improvement allocation. Previous treatments concentrate on defining optimal proportions to allocate resources and disregard the impacts of allocations to promote cooperation and are limited to static evaluations. Data Envelopment Analysis performs the decision-making units (DMUs) efficiency measurement. Methodological advances have resulted in models that analyze their internal structure and temporal impacts on efficiency. We propose an integrated cooperative game and dynamic network DEA that considers known quantities of resources used in each stage and the time effects to optimize the system’s profit. Each DMU stage is a player, and we investigate performance before and after resource sharing. Using Shapley value and Nucleolus, it is possible to allocate the benefits obtained based on the marginal contributions of each stage, providing incentives to motivate and maintain cooperation. A numerical example is used to illustrate the method. The results confirm the identification of inefficient DMUs and that sharing resources allows for profit increase for all of them.

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“…Lozano et al. 25 reviewed some transferable utility (TU) games and Nash bargaining games for combining the DEA model with game theory approach. Li et al.…”

Section: Literature Reviewmentioning

confidence: 99%

Use Shapley value for increasing power distinguish of data envelopment analysis model: An application for estimating environmental efficiency of industrial producers in Iran

Omrani

Amini

Babaei

et al. 2019

Energy & Environment

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Data envelopment analysis is a linear programming model for estimating the efficiency of decision making units (DMUs). Data envelopment analysis model has two major advantages: it does not need the explicit form of production function for estimating the efficiency scores of decision making units and also, it allows decision making units to choose the weights of inputs and outputs to reach the estimated efficient frontier. In several cases, the distinguish power of data envelopment analysis model is weak and it is unable to rank decision making units, entirely. The goal of this study is to provide a better methodology to fully rank all the decision making units. First, the efficiency scores of all decision making units are generated using the cross-efficiency data envelopment analysis model and then, the cooperative game theory approach is applied to produce a fully fair ranking of decision making units. The DEA-Game model calculates the Shapley value for each coalition of decision making units and the final ranking is relied on common weights. These fair common weights are found using the Shapley value to rank decision making units, completely. To illustrate the capability of the proposed model, the industrial producers in the provinces of Iran are evaluated. First, the suitable indicators are defined and then, the actual environmental data for year 2013 is gathered. Finally, the proposed model is applied to fully rank the industrial producers in provinces of Iran from environmental perspective. The results show that the DEA-Game model can rank provinces, entirely. Based on the results, the industrial producers in big provinces such as Tehran, Fars and Yazd have undesirable performance in environmental efficiency.

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DEA and Cooperative Game Theory

Cited by 9 publications

References 65 publications

Ranking efficient DMUs using cooperative game theory

Ranking efficient DMUs using cooperative game theory

Allocating Benefits Due to Shared Resources Using Shapley Value and Nucleolus in Dynamic Network Data Envelopment Analysis

Use Shapley value for increasing power distinguish of data envelopment analysis model: An application for estimating environmental efficiency of industrial producers in Iran

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