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Minimax Theorem Application

Hard · Game Theory & Logic · Quant Trader interview question · game-theory, minimax-theorem, zero-sum-game, optimization

Two traders, Alice and Bob, are playing a zero-sum game. Alice chooses a row (strategy x) from a 2x2 payoff matrix, and Bob independently chooses a column (strategy y). The payoff matrix represents the amount Bob pays Alice, $f(x, y)$. Alice aims to maximize her payoff, while Bob aims to minimize it. The payoff matrix is: Let $V_A$ be Alice's optimal expected payoff when she maximizes her minimum payoff, and $V_B$ be Bob's optimal expected payoff when he minimizes his maximum payoff. According t