|
Contributions to Game Theory and Management, 2007, том 1, страницы 152–167
(Mi cgtm10)
|
|
|
|
PGN-Value for Dynamic Games with Changing Partial Cooperation
Hong-Wei Gao, Ye-Ming Dai, Qian Wang College of Mathematics, Qingdao University, Qingdao, 266071, P. R. China
Аннотация:
The game with partial cooperation with perfect information
in extensive form is considered. The optimal solution PMS-vector in
such a game has been proposed in [Petrosjan, 2000].
In our paper the characteristic functions are defined for each coalition
$S$ $(S\subset N)$ according to some unified principle (for example, the best
response to Nash equilibrium), but they are not necessarily supper
additive.
A new principle of optimal behavior in such a game is established, based
on the nucleolus as optimality principle for the allocation of coalitional
payoff. On the first part of this paper, we have made an assumption
that once the player announced that he would take cooperative behavior
and never change this announcement, namely, he could not leave the
coalition.
Based on this assumption, we construct algorithm for the solution of
the game. And in the second part in this paper, we try to eliminate
this limitation and, so, we construct a new method to achieve the goal.
Algorithm of $PGN$-value of this kind of a game is offered and the optimal trajectory is found. The existence and uniqueness of nucleolus
leads to the existence and uniqueness of the new solution.
Ключевые слова:
Game with changing partial cooperation, nucleolus, Nash equilibrium, perfect information, $PGN$-value.
Образец цитирования:
Hong-Wei Gao, Ye-Ming Dai, Qian Wang, “PGN-Value for Dynamic Games with Changing Partial Cooperation”, Contributions to Game Theory and Management, 1 (2007), 152–167
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/cgtm10 https://www.mathnet.ru/rus/cgtm/v1/p152
|
|