Witsenhausen Counterexample: Optimal Strategy and Cost

Determine the optimal control strategies and exact minimum expected cost for the two-stage Witsenhausen problem x1 = x0 + u1, x2 = x1 + u2, where x0 ~ N(0, sigma^2), decision maker 1 observes x0 and incurs k u1^2, and decision maker 2 observes z2 = x1 + v with v ~ N(0,1) and incurs x2^2.

Source: Formal statement, Lecture 4 slide, 'Witsenhausen Problem (1968)'.

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