airfieldgame {TUGLab} | R Documentation |
Airfield game
Description
Given an airfield problem, this function returns the associated airfield game.
Usage
airfieldgame(c, binary = FALSE)
Arguments
c |
A vector of costs defining the airfield problem. |
binary |
A logical value. By default, |
Details
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).
Value
The characteristic function of the airfield game, as a vector in binary order if binary=TRUE
and in lexicographic order otherwise.
References
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.
See Also
Examples
c <- c(2000,3200,4100,5100)
airfieldgame(c,binary=TRUE)