GameTheoryAllocation-package {GameTheoryAllocation}

Tools for Calculating Allocations in Game Theory

Description

Many situations can be modeled as game theoretic situations. Some procedures are included in this package to calculate the most important allocations rules in Game Theory: Shapley value, Owen value or nucleolus, among other. First, we must define as an argument the value of the unions of the envolved agents with the characteristic function.

Author(s)

A. Saavedra-Nieves

Maintainer: A. Saavedra-Nieves ([e-mail])

References

Frisk, M., Gothe-Lundgren, M.,Jornsten, K., Ronnqvist, M. (2010). Cost allocation in collaborative forest transportation. European Journal of Operational Research, Vol. 205, pp. 448-458.

Gillies, D.B. (1953). Some theorems on n-person games. PhD thesis, Princeton University.

Owen, G. (1977). Values of games with a priori unions. Mathematical Economics and Game Theory: Essays in Honor of Oskar Morgenstern (Eds.: O. Moeschlin R. Hein). Springer, New York.

Shapley, L.S. (1953). A value por n-person games. In H. Kuhn y A. Tucker (eds), Contributions to the theory of games II, Vol. 28, Annals of Mathematics Studies. Princeton University Press.

Schmeidler, D. (1969). The nucleolus of a characteristic function game, SIAM Journal of Applied Mathematics, vol. 17, pp. 1163-1170.

Examples

# Example 1

characteristic_function<-c(0,0.538, 0.761, 1.742, 0.554, 0.137, 0.293, 0.343)
isinthecore(characteristic_function,allocation=c(0.1,0.2,0.043),game="cost")
#[1] "The allocation is not in the core"
#NULL

isinthecore(characteristic_function,allocation=c(0.05,0.206,0.087),game="cost")
#[1] "The allocation is in the core"
#NULL

nucleolus(characteristic_function,game="cost")
#[1] "Nucleolus"
#      1     2 3
#  0.137 0.206 0
# Example 2

characteristic_function<-c(1,1,2,1,2,2,2)
Owen_value(characteristic_function,union=list(c(1,2),c(3)),game="cost")
#[1] "Owen Value"
#     1    2   3
#  0.25 0.25 1.5