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Difficulty: Hard
Category: Game Theory & Logic
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: 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
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