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.
Citation
Man-Chung Ng. Chi-Ping Mo. Yeong-Nan Yeh. "ON THE CORES OF SCALAR MEASURE GAMES." Taiwanese J. Math. 1 (2) 171 - 180, 1997. https://doi.org/10.11650/twjm/1500405235
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