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Defender Acts 1st

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

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  1. 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]

  2. Minimax Strategy Random Cost Matrix Expected Cost Matrix

  3. Minimax Strategy Example: Ci,j=N(mi,j, si,j) Random Cost Matrix Expected Cost Matrix

  4. 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

  5. Banks and Anderson Strategy #1 D*=argmaxiP(C*i < mink C*k) Choose D1, but rather close to indifferent

  6. 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

  7. 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]

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