The core of a class of non-atomic games which arise in economic applications
AbstractWe prove a representation theorem for the core of a non-atomic game of the form v = fOil, where Il is a finite dimensional vector of non-atomic measures and f is a non-decreasing continuous concave function on the range of Il. The theorem is stated in terms of the sub gradients of the function f. As a consequence of this theorem we show that the game v is balanced (i. e., has a non-empty core) iff the function f is homogeneous of degree one along the diagonal of the range of Il, and it is totally balanced (i.e., every subgame of v has a non-empty core) iff the function f is homogeneous of degree one in the entire range of Il. We also apply our results to some non-atomic games which occur in economic applications.
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Non-atomic games; Market games; Core;
Other versions of this item:
- Diego Moreno & Benyamin Shitovitz & Ezra Einy, 1999. "The core of a class of non-atomic games which arise in economic applications," International Journal of Game Theory, Springer, vol. 28(1), pages 1-14.
- Einy, Ezra & Moreno, Diego & Shitovitz, Benyamin, . "The core of a class of non-atomic games which arise in economic applications," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4221, Universidad Carlos III de Madrid.
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