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Defender's Strategy Selection: A Cost-Oriented Decision-Making Matrix Example

This study explores the concepts of defender strategies based on random and minimax cost matrices. It delves into selecting the optimal strategy using expected cost matrix calculations. By comparing various minimax and random strategies, it determines the most advantageous actions for the defender. The analysis involves examining costs, strategies, and expected outcomes to guide the defender towards optimal decision-making in strategic scenarios.

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Defender's Strategy Selection: A Cost-Oriented Decision-Making Matrix Example

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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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