第10章对策论

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2 α, α,, α n β, β,, βn ( a, β ) α (α ) 0-0- n n n n n

3 α α A α α α α n α α α α n A = α α α αn α α α αn A = ( α ) n α α α α n α α α α n B = α α α αn α α α αn B = ( α ) S n { } S = α, α,, α S { } S = β, β,, βn {,, } = S S A - 0-

4 = S S {,, } = S S A ={ } 0 A = { } = S, S, A { α, α, α, α } S = 3 4 { β, β, β } S = A = α β α -5 α α 3 α β β β 3

5 nα = α ( =,,, ) V = ax(n α ) = axα = V axα α = ( =,,, ) V = n(ax α ) = nα = V V

6 V = ax(n α ) = n(ax α ) V = V V V V V V V V V α β 3 a β ( a, β ) ( a, β ) V = V { } 0.- = S, S, A ( a, β ) =,,,=,, n a a a a a a ax a n a a a ax a a n a n ax a ax a n a ax n a n ax a a ax n a axna naxa

7 ax n a = n ax a = a a = a a = n ax n a n ax a = n a = ax a a = ax n a = n ax a x a = n ax a = ax a a a = ax n a = n a a a a a =,,,=,, n V = ax n a = V = n ax a = 3 V V β β 0-4 α α p α p α β β p = p q = q q q

8 V = E( p, q) = 3 pq + ( ) pq 4pq + 5pq = 3 p q + ( ) p ( p ) 4( p ) q + 5( p )( p ) = 4 pq 7 p 9q = 4( p )( q ) p = α 4 β 9 5 p = { p, p} =, 4 4 q= { q, q} =, V = { } p = p, p,, p = p =, p 0 { } q = q, q,, qn n = q =, q 0 V E( p, q) a pq = = = = n 0.3 V α β 0.3.

9 A a a = a a V = {, }, = {, q } p p p q q a pq + a pq + a pq + a pq = V p ( a q + a q ) + p ( a q + a q ) = V p > 0, p + p =, a q + a q = V aq + aq = V q > 0, q + q = a p + a p = V a p + a p = V V = 7 3 p = p = 4 4 3q+ 4q = V 5q+ q = V q + q = q = q = 3p+ 5p = V 4p+ p = V p+ p = 3 p =, 4 4

10 q =, 7 V = 0.3. n V = n{ a p + a p } p = p V = n{( a a) p + a } p = p = 0-0 p 3 V p p ( ) = 5 + V p p ( ) = 3 +

11 5 7 p =, p =, V = p =, Q = 0,,, n A a a K a > a K K a a L L a < a L 0.3- A,,, K p = p = = = 0 p K A

12 A= ( a ) a a a a a a A a a a n n = n a p + a p + + a p V a p + a p + + a p V anp+ anp + + anp V p+ p + + p = aq + aq + + a nqn V aq + aq + + anqn V a q+ aq+ + anqn V q + q + + qn = 0.3- V

13 a p V ( =,,, n) = p =, p 0 = n aq V ( =,,, ) = n q =, q 0 = V > 0 p x = ( =,,, ) V y q = ( =,,, n ) V ax ( =,,, n) = x = = V x 0 ( =,,, ) ay ( =,,, ) = y = = V y 0 ( =,,, n) = x + x + + x V y y y V = () x, x,, x, n

14 ax ( =,,, n) = x 0 f x x x x ( ) = () y, y,, yn, n y = ay ( =,,, ) 0 f y y y y ( ) = n p+ p + 5p3 V p+ 3p + 4p3 V 3p+ 4p + p3 V p+ p + p3 3q+ q + 3q3 V q+ 3q + 4q3 V 5q+ 4p + p3 V q+ q + q3 p x = ( =,,, ) V y q = ( =,,, n ) V

15 3x+ x + 5x3 x+ 3x + 4x3 3x+ 4x + x3 x 0 ( =,, 3) 3y+ y + 3y3 y+ 3y + 4y3 5y+ 4y + y3 y 0 ( =,, 3) V V ()x ( =,,3) 3x+ x + 5x3 x+ 3x + 4x3 3x+ 4x + x3 x 0 ( =,, 3) f ( X) = x + x + x 3 () y, y, y 3 3y+ y + 3y3 y+ 3y + 4y3 5y+ 4y + y3 y 0 ( =,, 3) f ( Y) = y + y + y 3 3 x = 0, x =, x3 = V = = x + x + x p = 0, p = =, p3 = =, p = 0,, 5 5 V = q = { q, q, q3} =,0, 5 5

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第10章 对策论

第10章对策论