Strict convexity of the objective function and uniqueness of the maximum point in a model with three arbitrary random priorities

The main result of this paper is the proof of the strict concavity of some function of integral form depending on three random variables, which we call priorities. This function is an objective function in the so-called model with priorities, in which the arbiter, following expert opinions, distributes funds among the enterprises and institutions under his jurisdiction. This result implies an important corollary about the existence and uniqueness of a local maximum point (which is also a global maximum point) of the objective function. This is a significant generalization of the corresponding result of N.V. Neumezhitskaia, S.I. Uglich and T.A. Volosatova, published in December 2020.

On randomized Cobb-Douglas production function

The paper considers a Cobb-Douglas function with n random elasticities. A theorem on the concavity and strict concavity of such a function is proved.

A Rent-Seeking Framework for Multipath TCP

Network utility maximization (NUM) for Multipath TCP (MPTCP) is a challenging task, since there is no well-defined utility function for MPTCP [6]. In this paper, we identify the conditions under which we can use Kelly's NUM mechanism, and explicitly compute the equilibrium. We obtain this equilibrium by using Tullock's rent-seeking framework from game theory to define a utility function for MPTCP. This approach allows us to design MPTCP algorithms with common delay and/or loss constraints at the subflow level. Furthermore, this utility function has diagonal strict concavity, which guarantees a globally unique (normalized) equilibrium.

A Note on Concavity Conditions of Cobb–Douglas and CES Production Function with at Least Two Inputs

In microeconomics, the strict concavity is a very important property of a production function. In 2010, Avvakumov et al. gave a necessary and sufficient condition for the strict concavity of the Cobb–Douglas and constant elasticity of substitution (CES) production function with at least two inputs. To derive these conditions, the negative definiteness of the Hessian for both production functions was examined using certain recurrences for the principal corner minors. The purpose of this note is to complement the proof of Avvakumov, Kiselev, Orlov & Taras’ev ( 2010 , Computational Mathematics and Modeling, 21(3), 336–378) by showing that the use of recurrences and mathematical induction is not necessary, and that a necessary and sufficient condition for the strict concavity can be obtained by considering a particular square matrix, whose determinant can be calculated directly using the rule for the determinant of a lower or upper triangular matrix. JEL codes: C60, C65, D21, D24

On the Openness of Unique Pure-Strategy Nash Equilibrium

This paper investigates whether small perturbations to a game with continuous strategy spaces and unique Nash equilibrium also yields a game with unique equilibrium. The answer is affirmative for games with smooth payoffs, differentiable strict concavity in own actions, and transversal intersection of best response curves. Though intuitive for games with unique interior equilibrium, this result holds even for equilibria at the boundaries of strategy sets.

A Folk Theorem for Repeated Elections with Adverse Selection

This article establishes a folk theorem for a model of repeated elections with adverse selection: when citizens (voters and politicians) are sufficiently patient, arbitrary policy paths through arbitrarily large regions of the policy space can be supported by a refinement of perfect Bayesian equilibrium. Politicians are policy motivated (so office benefits cannot be used to incentivize policy choices), the policy space is one-dimensional (limiting the dimensionality of the set of utility imputations), and politicians’ preferences are private information (so punishments cannot be targeted to a specific type). The equilibrium construction relies critically on differentiability and strict concavity of citizens’ utility functions. An extension of the arguments allows policy paths to depend on the office holder's type, subject to incentive compatibility constraints.