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2786Uniform Mixing in a 3x3 Guessing GameConsider the zero-sum matrix with payoff +1 on the diagonal and -1 off the diagonal: \[ \begin pmatrix 1 & -1 & -1 \\ -1 & 1 & -1 \\ -1 & -1 & 1 \end pmatrix . \] Find the mixed equilibrium and the value.脑筋急转弯中等derivation未尝试面试订阅2787Why Pure Saddle Points Already Solve the Mixed GameSuppose a finite zero-sum matrix game has a saddle point at entry (i \*,j \*). Explain why allowing mixed strategies cannot improve either player's outcome beyond that same value.脑筋急转弯中等derivation未尝试面试订阅2788Search Three Targets With Values 5, 3, and 2A defender can inspect exactly one of three targets. If the attacker chooses the inspected target, the defender earns the target's value; otherwise the defender gets 0. The target values are 5, 3, and 2. Find the defender's optimal inspection mix and the value.脑筋急转弯中等derivation未尝试面试订阅2789Duplicate Rows Do Not MatterSuppose a zero-sum matrix has two identical rows. Explain why deleting one of the duplicate rows cannot change the value of the game.脑筋急转弯简单derivation未尝试面试订阅2790A Safe Strategy Creates Multiple EquilibriaConsider the zero-sum game \[ \begin pmatrix 1 & -1 \\ 0 & 0 \\ -1 & 1 \end pmatrix . \] Find the value of the game and describe at least one optimal strategy for each player.脑筋急转弯中等derivation未尝试面试订阅