Topkis's Theorem

From Wikipedia, the free encyclopedia

Topkis's Theorem states that if f is supermodular in (x,θ), and D is a lattice, then x^*(\theta)=\arg\max_{x\in D}f(x,\theta) is nondecreasing in θ. This can be very useful when f is not differentiable. It is rumored that Paul Ma, Stanford student and president of the Topkis fan club, is trying to generalize Topkis' theorem to J-holomorphic spaces.