Given an airfield problem, this function returns the associated airfield game.
airfieldgame(c, binary = FALSE)The characteristic function of the airfield game, as a vector in binary order if binary=TRUE and in lexicographic order otherwise.
A vector of costs defining the airfield problem.
A logical value. By default, binary=FALSE.
Let \(N = \{1, \dots, n\}\) denote a set of agents, and let \(c \in \mathbb{R}_+^N\) be a cost vector. Each \(c_i\) represents the cost of the service required by agent \(i\). Segmental costs are defined as the difference between a given cost and the first immediately lower cost: \(c_i - c_{i-1}\) for \(i \in N \backslash \{1\}\).
Each \(c \in \mathbb{R}_+^N\) defines an airfield problem, which is associated to an airfield game \(v_{a}\in G^N\), is defined by $$v_{a}(S)=\max\{c_j:j\in S\}\text{ for all }S\in 2^N.$$
Airfield games, as defined, are cost games, but they can also be expressed as savings games. Additional tools and methods for addressing airfield problems are available in the AirportProblems package Bernárdez Ferradás et al. (2025).
Bernárdez Ferradás, A., Sánchez Rodríguez, E., Mirás Calvo, M., & Quinteiro Sandomingo, C. (2025). AirportProblems: Analysis of Cost Allocation for Airport Problems. R package version 0.1.0. https://CRAN.R-project.org/package=AirportProblems
Littlechild, S.C., & Owen, G. (1973). A Simple Expression for the Shapely Value in a Special Case. Management Science, 23, 370-372.
claimsgame, savingsgame
c <- c(2000,3200,4100,5100)
airfieldgame(c,binary=TRUE)
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