= Max-n search
{title2=$\max^n$}
<Backward induction> with an $n$-component <utility> vector. At a node controlled by player $i$, evaluate each child, choose a child maximizing coordinate $i$ and copy its entire vector. A fixed tie rule makes the returned vector well defined. By <mathematical induction> from terminal positions, the selected continuation is a best response at every node of a finite <perfect-information game>, giving a <pure strategy> <subgame perfect equilibrium>. The vector must be copied intact; separate coordinatewise maxima need not describe any attainable outcome.
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