It is known that a central configuration of the planar four body problem consisting of three particles of equal mass possesses a symmetry if the configuration is convex or is concave with the unequal mass in the interior. We use analytic methods to show that besides the family of equilateral triangle configurations, there are exactly one family of concave and one family of convex central config...

We present a simple convexity argument that clarifies the effectiveness and scope of Sannikov’s approach [S] to continuous time principal-agent problems. We in particular stress the importance of the appropriate concavity of the agent’s running payoff function as a function of his actions.

In this paper a Radner economy is considered with Uncertainty, modeled by means of the Choquet Expected Utility. Agents are split into two categories: optimists, who hold a concave capacity, and pessimists, who hold a convex one. A no trade theorem is stated and proved under the assumption of common beliefs with uncertainty.

If the value cumulative distribution functions are strictly log-concave at the highest lower extremity of their supports, a simple geometric argument establishes the uniqueness of the equilibrium of the first-price auction in the asymmetric independent private values model.  2005 Elsevier Inc. All rights reserved. JEL classification: D44

We prove small-deviation estimates for the volume of random convex sets. The focus is on convex hulls and Minkowski sums of line segments generated by independent random points. The random models considered include (Lebesgue) absolutely continuous probability measures with bounded densities and the class of log-concave measures.

It is shown that, if ν ≥ 1/2 then the generalized Marcum Q function Qν(a, b) is log-concave in b ∈ [0,∞). This proves a conjecture of Sun, Baricz and Zhou (2010). We also point out relevant results in the statistics literature.