Diagonally strictly concave
WebPrinceton University 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 …
Diagonally strictly concave
Did you know?
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 … WebNov 20, 2016 · Concave games provide an attractive setting for many applications of differential games in economics, management science and engineering, and state coupling constraints happen to be quite natural...
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+ 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 …
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. 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}.
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 …
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, how to reward team performanceWebAug 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 … northern alberta jubilee auditorium careersWebGeneralising Diagonal Strict Concavity Property for Uniqueness of Nash Equilibrium Eitan Altman, Manjesh Kumar Hanawal, and Rajesh Sundaresan Abstract In this paper, we … northern alberta institute of technology naitWebGENERALISING DIAGONAL STRICT CONCAVITY PROPERTY 219 A sufficient condition for the familyVto be diagonally strictly concave (convex) for a given r ‚0 is that the … how to reward employees1. 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. northern alberta jubilee auditorium ticketsWebOct 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 ... northern alberta jubileeWebMay 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]. northern alberta outfitters