13880721(Farzaneh Ghayour Baghbani)

13880721(Farzaneh Ghayour Baghbani) - / / : : ( minmax ) ....

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Unformatted text preview: / / : : ( minmax ) . pure N.E . NP-Complete zero-sum . maxmin NE , C, .( . . . [0,1] . . PY X .( . PX B . PX . Pure NE NP-complete PY PX P'X Nash Pure NE . . PY X NE P'X PY : PX pure NE PX : PX > ( NE : A .( C B A ) ) (Y X) B . Nash . ( . NP-hard . . . . . . NP NP-complete ) .( P NP-complete , . Pure NE NP , NP-complete NP . . NP-complete NP-complete NP-complete NP , , Pure NE utility . T 3Ci : if if if . Ci : Pure NE NP NP-complete Pure NE . .. NP-complete : Pure NE Utility 3-SAT Z Y X 3-SAT F Utility . Bi Ai SAT U(Ai) = 1 U(Ai) = 1 U(Ai) = -1 U(Bi) = 1 U(Bi) = -1 U(Bi) = 1 Ci=T Ci=F and Ai≠Bi Ci=F and Ai=Bi Ci=T Ci=F and Ai≠Bi Ci=F and Ai=Bi Ci=F T F T F -, ,,-, if if if Ci=T T F T F . . ( von Neuman Ci=T Pure NE , , , , , NE 3-SAT Zero Sum Zero Sum . ) maxmin minmax . q 1-q p 1-p : 3q+1-q=2q+4-4q 3p+2-2p=p+4-4p . Zero Sum minmax maxmin ) von Neuman minmax maxmin => => q= p= Mixed NE . min {3q+1-q,2q+4(1-q)} max q min {33q+1-q,2q+4(1-q)} minmax maxmin , utility NE ( minmax maxmin : maxmin V utility utility . : maxs1 maxmin : mins2 (U1 (S1,S2)) ≥ V . : p1 maxmin q1 q2 p2 : max λ1 3q1 + q2 ≥ λ1 2q1 + 4q2 ≥ λ1 q1 + q2=1 : min λ2 3p1 +2 p2 ≤ λ2 p1 + 4p2 ≤ λ2 p1 + p2 = 1 . LP ...
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