Pointwise minimum (source code)

= Pointwise minimum
{title2=$(f\wedge g)(x)=\min\{f(x),g(x)\}$}

The <function> taking the lesser value at every common-domain point. It forms the lower envelope of two graphs. For finitely many <affine functions> it is a <concave function>: each affine branch is at least the corresponding <convex combination> of the two endpoint minimum values, so taking the minimum preserves that lower bound. A maximizing <mixed strategy> in a two-player <zero-sum game> maximizes such a lower envelope of opposing pure-choice <expected payoffs>.