Diagonally strictly concave

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August undefined, 2024

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. WebPrinceton University

GENERALISING DIAGONAL STRICT CONCAVITY …

WebSep 29, 2024 · 1. I will answer some of your questions. The entries of a Hessian matrix H of f are second partials H i j = ∂ i ∂ j f and it is a standard result in multivariable calculus that ∂ i ∂ j f = ∂ j ∂ i f provided both second partials are continuous functions. In your case, the entries of the Hessian are constants so are continuous functions. WebNov 25, 2024 · 1 Answer Sorted by: 2 Yes if we assume that f ″ ( x) < 0 esists then f ( x) is strictly concave but if f ( x) is strictly concave we can also have f ″ ( x) ≤ 0 with f ″ ( x) … church designer near me

Existence and Uniqueness of Equilibrium Points for …

Web(b) f is strictly convex i for any a;b2C and any 2(0;1), the above inequality is strict. The following equivalence is immediate from the de nitions. Theorem 1. Let C RN be non-empty and convex and let f: C!R. fis convex i fis concave. fis strictly convex i fis strictly concave. f is both concave and convex i for any a;b2RN and any 2(0;1), f( a+ WebJun 1, 2015 · The conflict network game satisfies the requirement of a concave n-person game by the assumptions on the payoff function. Hence, the following proposition establishes existence and uniqueness by proving that the conflict network game is also diagonally strictly concave. Proposition 1 There exists a unique equilibrium in the … http://www.lamda.nju.edu.cn/chengq/course/slides/Lecture_4.pdf deutsche bank advisory board

Generalising diagonal strict concavity property for …

Defintion of strictly concave - Mathematics Stack Exchange

Web(Indian Institute of Technology Bombay) Rajesh Sundaresan (Indian Institute of Science) Registered: Abstract In this paper, we extend the notion of diagonally strictly concave … WebOct 21, 2013 · When the strategy sets S i are one-dimensional, the condition implies that the payoff functions are diagonally strictly concave. Denote G(s) the Jacobian of ∇u(s). It is straightforward to show that if G(s) + G(s) T is negative definite for any s ∈ S, then the payoff functions are diagonally strictly concave. Some additional technical ... deutsche bank account typesWebIndian J. Pure Appl. Math., 47(2): 213-228, June 2016 c Indian National Science Academy DOI: 10.1007/s13226-016-0185-4 GENERALISING DIAGONAL STRICT CONCAVITY PROPERTY FOR UNIQUENESS OF NASH ... deutsche bank africa foundation

"WebProposition 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, " - Diagonally strictly concave

Diagonally strictly concave

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 ; 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].

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WebStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, … WebIndian J. Pure Appl. Math., 47(2): 213-228, June 2016 c Indian National Science Academy DOI: 10.1007/s13226-016-0185-4 GENERALISING DIAGONAL STRICT CONCAVITY …

WebGeneralising Diagonal Strict Concavity Property for Uniqueness of Nash Equilibrium Eitan Altman, Manjesh Kumar Hanawal, and Rajesh Sundaresan Abstract In this paper, we … 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.

1. A differentiable function f is (strictly) concave on an interval if and only if its derivative function f ′ is (strictly) monotonically decreasing on that interval, that is, a concave function has a non-increasing (decreasing) slope. 2. Points where concavity changes (between concave and convex) are inflection points. Web40 x 2 y − 10 − 64 x 2 y − 10 = − 24 x 2 y − 10 ⩽ 0 which means f ( x, y) is concave. Since f ( x, y) is nonlinear, it cannot be both convex and concave, and there must be something wrong with the derivation above. I would like to ask which part of my under standing is wrong. Thank you. convex-analysis convex-optimization hessian-matrix Share Cite

WebJun 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 …

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 … church design resourcesWebSep 8, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site deutsche bank account opening onlineWebIt is shown that for a strictly con-cave game the system is globally asymptotically stable with respect to the unique equilibrium point of the game. Finally, it is shown how a … church design plans 200 seatsWebJ. 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 … church designs and plansWebJun 1, 2016 · Generalising diagonal strict concavity property for uniqueness of Nash equilibrium CC BY-NC-SA Authors: Eitan Altman National Institute for Research in … church design software free downloadWebJul 1, 2009 · Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 33 (1965), pp. 520-534. CrossRef Google Scholar [44] W.H. Sandholm. Potential games with continuous player sets. J. Econ. Theory, 97 (2001), pp. 81-108. View PDF View article View in Scopus Google Scholar [45] church designs interiorWebGENERALISING DIAGONAL STRICT CONCAVITY PROPERTY 219 A sufﬁcient condition for the familyVto be diagonally strictly concave (convex) for a given r ‚0 is that the … church designs exterior old