## Taiwanese Journal of Mathematics

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

### ON THE CORES OF SCALAR MEASURE GAMES

Man-Chung Ng, Chi-Ping Mo, and Yeong-Nan Yeh

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.11650/twjm/1500405235

**Mathematical Reviews number (MathSciNet)**

MR1452094

**Zentralblatt MATH identifier**

0882.90143

**Keywords**

convex games exact games cores scalar measure games vector measure games core expansion core geometryb

#### 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