Facultade de Fisioterapia

Airport games: The core and its center

González-Díaz, Julio; Mirás-Calvo, Miguel A.; Quinteiro-Sandomingo, Carmen; Sánchez Rodríguez, Maria Estela
Abstract:
An approach to define a rule for an airport problem is to associate to each problem a cooperative game, an airport game, and using game theory to come out with a solution. In this paper, we study the rule that is the average of all the core allocations: the core-center (González-Díaz and Sánchez-Rodríguez, 2007). The structure of the core is exploited to derive insights on the core-center. First, we provide a decomposition of the core in terms of the cores of the downstream-subtraction reduced games. Then, we analyze the structure of the faces of the core of an airport game that correspond to the no-subsidy constraints to find that the faces of the core can be seen as new airport games, the face games, and that the core can be decomposed through the no-subsidy cones (those whose bases are the cores of the no-subsidy face games). As a consequence, we provide two methods for computing the core-center of an airport problem, both with interesting economic interpretations: one expresses the core-center as a ratio of the volume of the core of an airport game for which a player is cloned over the volume of the original core, the other defines a recursive algorithm to compute the core-center through the no-subsidy cones. Finally, we prove that the core-center is not only an intuitive appealing game-theoretic solution for the airport problem but it has also a good behavior with respect to the basic properties one expects an airport rule to satisfy. We examine some differences between the core-center and, arguably, the two more popular game theoretic solutions for airport problems: the Shapley value and the nucleolus.
Year:
2016
Type of Publication:
Article
Journal:
Mathematical Social Sciences
Volume:
82
Pages:
105-115
Month:
July
DOI:
https://doi.org/10.1016/j.mathsocsci.2016.04.007
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