# Game Theory 0-Sum Games

**Tutor description**

Solution: (a). Column 2 dominates column 1; then row 3 dominates row 4; then column 4 dominates column 3; then row 1 dominates row 2. The resulting submatrix consists of row 1 and 3 vs. columns 2 and 4. Solving this 2 by 2 game and moving back to the original game we find that value is 3/2, I’s optimal strategy is p (1 2, 0,1 2,0) and II’ (0,3 8, 0,5 8). (b). Column 2 dominates column 4; then (1/2)row 1+ (1/2)row 2 dominates row 3; then (1/2)col 1+(1/2)col 2 dominates col 3. The resulting 2 by 2 game is easily solved. Moving back to the original game we find that the value is 30/7, Is optimal strategy is q ’s optimal strategy is (2/7,5/7,0) and II’s optimal strategy is (3/7,4/7,0,0).

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