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Defender Acts 1st. Random Cost Matrix Expected Cost Matrix. where C i,j =Cost to defender from play (A j |D i ). where m i,j =E[C i,j ]. Minimax Strategy. Random Cost Matrix Expected Cost Matrix. Minimax Strategy. Example: C i,j =N( m i,j , s i,j ).

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defender acts 1st
Defender Acts 1st

Random Cost Matrix Expected Cost Matrix

where Ci,j=Cost to defender from play (Aj|Di)

where mi,j=E[Ci,j]

minimax strategy
Minimax Strategy

Random Cost Matrix Expected Cost Matrix

minimax strategy1
Minimax Strategy

Example: Ci,j=N(mi,j, si,j)

Random Cost Matrix Expected Cost Matrix

minimax strategy2
Minimax Strategy

Example: Ci,j=N(mi,j, si,j)

Random Cost Matrix Expected Cost Matrix

Which action should Defender take?

D*=argminimaxj E[Ci,j]

=argminim*i

slide5

Banks and Anderson Strategy #1

D*=argmaxiP(C*i < mink C*k)

Choose D1, but rather close to indifferent

slide6

Banks and Anderson Strategy #2

Score(i)=mink {C*k} / C*i

Score(i) 2 (0,1] – Larger is better

E[Score(1)]=0.815

E[Score(2)]=0.822

D*=argmaxiE[Score(i)]

From this, choose D2

an alternative approach
An Alternative Approach

D*=argminiE[maxj Ci,j]

Choose D2, since worst case has lower expected cost

where m*i=E[C*i]=E[maxj Ci,j]