Diagonally strictly concave
WebAug 1, 1985 · Rosen proceeds by showing that the assumption of strictly diagonally concave payoff functions ascertains uniqueness of the equilibrium outcome. In the Appendix it is demonstrated that our model satisfies the condition for strict diagonal concavi- ty. At such an outcome no player can improve his payoff by a unilateral … Web𝑓is concave, if 𝑓 ñ ñ𝑥0 ℎis concave, ℎis nondecreasing in each argument, and 𝑔 Üare concave The general case is similar 𝑓ℎ∘𝑔 Lℎ :𝑔 5𝑥,…,𝑔 Þ𝑥 𝑓 ñ ñ𝑥𝑔 ñ𝑥 C 6ℎ𝑔𝑥𝑔′ :𝑥 ; C 𝑔′′𝑥 ;
Diagonally strictly concave
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WebMay 15, 1988 · We say that {x, y} is (strictly) diagonally quasi-concave (DQCV) in y if -(x, y) is (strictly) DQCX in y. Remark 2.2. (i) In [3], we had called diagonal quasi …
WebPrinceton University WebWe say that a graph is concave up if the line between two points is above the graph, or alternatively if the first derivative is increasing. (In finance, such a curve is said to be convex.) Similarly, we say that a graph is concave down if the line between two points is below the graph, or alternatively if the first derivative is decreasing.
WebMay 15, 1988 · We say that {x, y} is (strictly) diagonally quasi-concave (DQCV) in y if - (x, y) is (strictly) DQCX in y. Remark 2.2. (i) In [3], we had called diagonal quasi-convexity the generalized-convexity (GCX) condition. It enabled us to generalize several theorems ofNikaido and Isoda for noncooperative N person games [8, 9]. WebJan 5, 2024 · Thus, J is a diagonal matrix with negative diagonal elements. This implies that J is negative definite. Henceforth [J+ \(J^T\)] is also negative definite, and according to Theorem (6) in, , the weighted sum of the utility functions \(\psi (q_{s},x)\) is diagonally strictly concave. Thus, the Nash equilibrium point is unique.
WebOptimization and concave/convex functions Examples: • The functions and are concave • The function is concave on its domain • Any affine function is both concave and convex …
Webstrictly concave and strictly convex functions. Theorem 6. Let Dbe an open convex subset of Rn and let f: D!R be a C2. Then 1. fis concave iff D2f(x) is a negative semidefinite matrix for all x2D. 2. fis convex iff D2f(x) is a positive semidefinite matrix for all x2D. 3.If D2f(x) is a negative definite matrix for all x2D, then fis strictly ... how do i print an attachment from an emailWebJun 30, 2016 · In this paper, we extend the notion of diagonally strictly concave functions and use it to provide a sufficient condition for uniqueness of Nash equilibrium in some … how do i print an email in outlookWebJan 1, 2024 · (Since h i is concave, it follows that the set S i is a convex set.) The next definition introduces the key condition used in establishing the uniqueness of a pure … how much money do wind turbines makeWebFeb 25, 2010 · (3), where hi is a concave function, and there exists some x˜i ∈ Rm i such that hi (x˜i) > 0. Assume also that the payoff functions (u1, ... , uI) are diagonally … how do i print an email from my iphoneWebStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, … how much money do wnba players make a yearWebJ. B. Rosen proved that in concave games of n players (which assumes that Cartesian product of strategy profiles is convex) if the game satisfies the condition of diagonally … how do i print addressed envelopes in wordWebProposition 8. The (twice continuously differentiable) function f : A ! R is concave if and only if D2 f (x) is NSD for every x 2A. If D2 f (x) is ND, then the function is strictly concave. Proof. We first show that concavity implies Hessian matrix is NSD. Suppose f is concave. Fix some x2A, with some z6= 0, take second-order Taylor expansion, how do i print an email message