Question

how do I solve this?

Lin 4. Ci C2 C3 C4 RI 2. 14 -1 -9 R2 0 0 0 0 R3 3 4 3 20 R4 -9 9-11

which out come would R pick. and why using dominance reasoning or the minimax equilibrium test?

Answer 1

dominance method Steps (Rule) Step-1: Step-2: 1. If all the elements of Column-i are greater than or equal to the corresponding elements of any other Column-j, then the Column-i is dominated by the Column-j and it is removed from the matrix. eg. If Column 2 Column-4, then remove Column-2 * 1. If all the elements of a Row-i are less than or equal to the corresponding elements of any other Row-j, then the Row- i is dominated by the Row-j and it is removed from the matrix. eg. If Row-3 Row-4, then remove Row-3 Again repeat Step-1 & Step-2, if any Row or Column is dominated, otherwise stop the procedure. Step-3: 2. Dominance rule to reduce the size of the payoff matrix Using dominance property Player B c, C, Cз с R, 2 14 1 19 R₂ o o o o Player A ' R3 3 4 3 20 R4 -9 9.11 row-2 row-3, so remove row-2, (2, 585:05 3,054,053,0 20) Player B C, C₂ C₃ C4 R, [2 14 -1.91 Player A R3 3 4 3 20 R4 - 99. 11 column-2 column-3, so remove column-2. (CZ 2 C3:14 2 - 1,4 2 3,92-1) Player B C₂ C₃ C4 R, 2 -1.91 Player A R3 3 3 20 R4 -9 -1 1

row-3 s row-2, so remove row-3, (R, SRG: -953, -15 3,1 s 20) Player B C₂ C₃ C4 R2 -1 -2 Player A R. 3 3 20 column-1 2 column-2, so remove column-1. (612 03:22 -1,323) Player B C3 C4 R][-1.9 Player A R33 20
now saddle point occur at (R3, C3). ( first choose the minimum of rows which is (-9, 3) and the maximum of column = (3, 20), intersection occur at 3 which is saddle point and corresponding R3 activity for player R.

therefore R will be pick R3

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