Taiwanese Journal of Mathematics

ON THE CORES OF SCALAR MEASURE GAMES

Abstract

A $CVM(k)$ game is a game of the form $f\circ \lambda$, where $\lambda$ is a $k$-dimensional non-atomic measure and $f$ is a continuously differentiable function on $R^k$. For a convex $CVM(1)$ game, we characterize the least upper bound'' and greatest lower bound'' of the core elements in terms of the distribution function. We also show that the core of a convex $CVM(1)$ game expands as the underlying measure $\lambda$ changes in a convex manner''. These results provide a partial geometric picture for the core and its variations of a convex $CVM(1)$ game.

Article information

Source
Taiwanese J. Math., Volume 1, Number 2 (1997), 171-180.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405235

Digital Object Identifier
doi:10.11650/twjm/1500405235

Mathematical Reviews number (MathSciNet)
MR1452094

Zentralblatt MATH identifier
0882.90143

Subjects
Primary: 90D12 90D13

Citation

Ng, Man-Chung; Mo, Chi-Ping; Yeh, Yeong-Nan. ON THE CORES OF SCALAR MEASURE GAMES. Taiwanese J. Math. 1 (1997), no. 2, 171--180. doi:10.11650/twjm/1500405235. https://projecteuclid.org/euclid.twjm/1500405235