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At every node, MAX would always move to maximise the minimum payoff while MIN choose to minimise the maximum payoff, hence there is nash equilibrium.

By using backwards induction, at every node, MAX and MIN player would act optimally. Hence, there is subperfect nash equilibrium.

How do I formally prove this?

Have you looked at this article http://math.ucr.edu/home/baez/games/games_18.html?

– nbro – 2020-05-29T18:41:47.243