Diagonally strictly concave
WebPrinceton University 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 …
Diagonally strictly concave
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WebFeb 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 … 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 ;
WebGeneralising Diagonal Strict Concavity Property for Uniqueness of Nash Equilibrium Eitan Altman, Manjesh Kumar Hanawal, and Rajesh Sundaresan Abstract In this paper, we … 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 …
WebJ. 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 … 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) …
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 ...
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, csds submission trackerWebIndian 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 ... dyson hot+cool ファンヒーター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 … csds statistics canadaWebMay 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]. dyson hot+cool ファンヒーター am 09 ibWebJan 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. csds statisticsWebNov 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. csds submission template1. 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. csds timetable