WebTheorem (Topkis). Let S be a sublattice of RN. Define S N ij ={x ∈ℜ (∃z ∈ S)x i = z i ,x j = z j } Then, S = I ij, S ij . Remark. Thus, a sublattice can be expressed as a collection of … WebFeb 14, 2016 · Although you are interested in the optimal value function, another tool that might be useful for your work is supermodularity which provides insight into monotonicity of optimal choice correspondence. In case of parameters, this concept is named increasing differences. In a nutshell, a function has increasing differences if $$ \frac {\partial^2 ...
Lecture 5: Monotone Compar. Statics
WebThe proof of Lemma 1 relies on Topkis’ theorem and the concept of stochastic dominance. Topkis’ theorem (Topkis 1998): Let f(a 1;a 2;x) : A 1 A 2 R !R, where A 1 and A 2 are nite ordered sets. Assume that f(a 1;a 2;x) (i) is supermodular in (a 1;a 2) and that (ii) has increasing di erences in (a 1;x) and (a 2;x):Then argmaxff(a 1;a 2;x) j(a ... WebAug 22, 2024 · 1 Answer. What the book calls the "Weierstrass Theorem" is more commonly known as the Extreme Value Theorem, which states that a continuous function defined on a compact domain attains a maximum and a minimum. A common proof of this theorem involves the use of the Bolzano–Weierstrass theorem, which you learned in your math … ossa lunghe esempio
Weierstrass Theorem in Optimization - Economics Stack Exchange
WebGetting to the heart of complementarity, Donald Topkis's book should be around for a long time. It will be of help in many fields in the social sciences ... with a generalisation of Tarski's fixed point theorem (section 2.5 of the book), which in contrast to Kakutani's fixed point theorem does not rely on the quasi- WebExplore key matchups, moves, and counters for Togekiss in Ultra League Premier. WebSee Answer. Question: 2. Consider the following version of Topkis theorem prove latter in the class, but you can also look at Sundaram's chapter in parameter monotonicity. The … ossa medical abbreviation