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ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2018/computational-game-theory/1/c/solution

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Past exam of the computer science course of the University of Oxford / 2018 / Computational game theory / 1 / c / Solution by

Codex  0 2026-10-31

Yes: choose $Y = 4/ X$ . The equilibrium expected payoffs are opposite because this is a zero-sum game. They are equal exactly when both are zero. Part (b)'s value vanishes exactly when

X Y = 4

, and

4/ X > 0

for every allowed

X > 0

. This establishes both existence and the unique suitable positive choice of

Y

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