Diagonally strictly concave
WebNov 23, 2024 · In an optimization problem, the decision maker seeks a maximizer (or minimizer) to an objective function, subject to some constraints. In a game, each player also optimizes her payoff, but the result depends on the strategies chosen by the other players. WebStrictly convex if strict inequality holds whenever x 6= y and 0 < λ < 1. We say f is concave if −f is convex. An affine function is both convex and concave. A function f is convex if it is convex when restricted to any line intersecting its domain: for any x ∈ domf and v, g(x +tv) is convex on {t : x +tv ∈ domf}.
Diagonally strictly concave
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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 ... 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.
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 WebGENERALISING DIAGONAL STRICT CONCAVITY PROPERTY 219 A sufficient condition for the familyVto be diagonally strictly concave (convex) for a given r ‚0 is that the …
WebPrinceton University http://www.lamda.nju.edu.cn/chengq/course/slides/Lecture_4.pdf
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.
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) … chubbs realtyWebIndian 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 ... designate meaning in lawWebSep 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 designated vs additional insuredWebJun 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 … designated title cedar hill texasWebJan 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 … chubbs pryor okWebMay 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 … chubbs realty group floridaWebGeneralising Diagonal Strict Concavity Property for Uniqueness of Nash Equilibrium Eitan Altman, Manjesh Kumar Hanawal, and Rajesh Sundaresan Abstract In this paper, we … chubb splash