This article is cited in
4 papers
On $k$-accessibility of the core of $TU$-cooperative game
Valery A. Vasil'ev Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
In the paper, a strengthening of the
core-accessibility theorem by the author is proposed. The results
obtained demonstrate that for any
$k \geq 1,$ and for any
imputation
$x$ outside of the nonempty core, a
$k$-monotonic
sequential improvement trajectory
$\{x_r\}_{r=0}^{\infty}$ with
$x_0 = x$ exists, which converges to some element of the core.
Here,
$k$-monotonicity means that for any
$r > 0,$ an imputation
$x_r$ dominates any preceding imputation
$x_{r-m}$ with
$r \geq m$
and
$m \in [1, k].$ Note that the core-accessibility theorem,
mentioned above, was established for the case
$k = 1$.
To show that
$TU$-property is essential to provide
$k$-accessibility of the core, we propose an example of
$NTU$-cooperative game
$G$ with a "black hole" being a closed
subset
$B \subseteq G(N)$ that doesn't intersect the core
$C(\alpha_G)$ and contains all the sequential improvement
trajectories originating at any point
$x \in B$.
Keywords:
domination, core, dynamical system, generalized Lyapunov function, $k$-accessibility.
UDC:
519.83
BBK:
22.18