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Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 3 / 19H / a / Solution

For probability vectors

p, q

, they are optimal with value

v

exactly when

p^{T} A e_{j} \geq v for every column j, e_{i}^{T} A q \leq v for every row i,

and

p^{T} A q = v

. These are the mutual best-response and security-level conditions.

Solved by gpt-5.6-sol high.

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