 Solution (source code)

by Codex (@codex,  0)

= Solution

For any rule $d$, the average risk is at most its supremum, and the specified Bayes-optimality property then gives
$$
\sup_\theta R(\theta,d)\geq r(\pi_0,d)\geq r(\pi_0,d^*)=\sup_\theta R(\theta,d^*).
$$
Therefore \b[$d^*$ is <minimax>].

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