Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc15776/doc.pdf Дата изменения: Mon Oct 29 13:03:06 2007 Дата индексирования: Mon Oct 1 20:37:43 2012 Кодировка:

.. () , . . N . -. . N , . POSITION GAMES WITH VECTOR-VALUED FUNCTION Fakhretdinova V.A. (Pskov) The problem of multistage process modelling is being investigated. The decisions are made successively in this process. The result of interaction for every person is presented in the limited set of criteria. The mathematical model of this problem is the position game N persons with vector-valued function. Nash-Pareto equilibrium is studied for the given set of problem. It's proved in the work that solution exist for position games with full memory having a vector-valued function, mixed strategies are possible. ( ) N , , . , 151


2. (I)

, . , . , , N = < G, A, P, U, f >, (1) G ­ ; A ­ , ; ­ ; U ­ , f i = f1i , ..., f lii ­

(

)

i- i N. : - -, , ; - -, N , ; , , ; - -, . , , [1] . , , -. i N si Si , f i ( s ) = f1i ( s ) , ..., flii ( s ) . . N [2].
152

(

)


.. -- -10, 2002, .151-153

1. s* S - ,
si Si , i = 1,..., N , f i (s * si ) f i (s *) , /

(2)

f i (s * si ) f (s *) , /

fi j (s * si ) fi j (s *), j = 1, ..., li ,

. - , i-, f i (s *) , , .
=< N , {S
i iN

}

, f i (s

{

)}iN

> . (3)

, s1 , s 2 , ... , s N S = S i . f i : S R li , -

(

)

f i (s ) = f1l1 (s ), ... , f lii (s

(

))

. (3), N [2]. G x. Gx G, x G , x. , x x D. x , D -. x Gx x. - D G/Gx, x, - D G.
153


2. (I)

2. s * - (1) -, x. i- i N ( ), . . (1) -, . . (1) N F i ( s ) =

f (s)
i j j=1

li

.

x , . x . x (s *)x , . F (s *)x = F 1 (s *)x , ... , F N (s *)x x . F (s *)x x D .
s * = (s *) , (s *)
D

(

)

. . , . s *= s x . s * x

(

x

)

(s *)D

. ,

()

x F i (s *)x F i (s * s

, . , s * - (1). , s * , i

)x

. -

, s * 154


.. -- -10, 2002, .151-155

(1), x , (2) i, j 1, ..., li f ji (s * si ) > f ji (s *) . ,
F i (s * si

)x

> F i (s *)x , , s * -

. , s * . , [1], . . 1. .. // . ­ .: , 1967. .13-40. 2. .. // -. 2001. .1 (21), .67-82.

155