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Difficulty: Hard
Category: Game Theory & Logic
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Topics: game-theory, probability, expected-value, market-microstructure
Two high-frequency trading firms, Alpha and Beta, are engaged in a 'War of Attrition' to capture a fleeting market opportunity. The market is worth a total of $V$ to the firm that remains in the market. Both firms incur a cost of $c$ per unit of time (e.g., per second) while participating in the contest. Assuming both firms play a symmetric mixed strategy equilibrium, what distribution governs the exit time of each firm?
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