Jane Street Quantitative Trader Interview Question: Solving Two-Player Zero-Sum Games
One classic area that often appears in interviews is the analysis and solution of two-player zero-sum games. In this comprehensive guide, we will dive deep into the methods for solving such games, understanding mixed strategies, and computing the value of the game — all skills crucial for both interviews and professional trading.
A two-player zero-sum game is a strategic scenario involving two players where one player's gain is exactly the other player's loss. In other words, the sum of the outcomes for both players is always zero. These games are fundamental in game theory, financial modeling, and are a staple in quantitative trading interviews.
Formally, if Player A and Player B are the two players, and if Player A gains $x$, then Player B loses $x$, so the total sum is zero:
