Central Economics and Mathematics Institute

About: Central Economics and Mathematics Institute is a facility organization based out in Moscow, Russia. It is known for research contribution in the topics: Population & Foreign-exchange reserves. The organization has 297 authors who have published 580 publications receiving 6449 citations. The organization is also known as: Federal State Institution of Science Central Economics and Mathematics Institute of the Russian Academy of Sciences.

Minimization of A Nondifferentiable Convex Function Defined not Everywhere

Abstract: We examine an oracle-type method to minimize a convex function f over a convex polyhedron G . The method is an extension of the level-method to the case, when f is a not everywhere finite function, i.e., it may equal to + X at some points of G . An estimate of its efficiency is given, and some modifications of the method are mentioned. Finally, we indicate possible ways of its employment and report results of a numerical experiment.

Variations of the v-Change of Time in Problems with State Constraints

Abstract: For a general optimal control problem with a state constraint, we propose a proof of the maximum principle based on a v-change of the time variable t ↦ τ, under which the original time becomes yet another state variable subject to the equation dt/dτ = v(τ), while the additional control v(τ) ≥ 0 is piecewise constant and its values are arguments of the new problem. Since the state constraint generates a continuum of inequality constraints in this problem, the necessary optimality conditions involve a measure. Rewriting these conditions in terms of the original problem, we get a nonempty compact set of collections of Lagrange multipliers that fulfil the maximum principle on a finite set of values of the control and time variables corresponding to the v-change. The compact sets generated by all possible piecewise constant v-changes are partially ordered with respect to inclusion, thus forming a centered family. Taking any element of their intersection, we obtain a universal optimality condition, in which the maximum principle holds for all values of the control and time.

Existence of the Nash-Optimal Strategies in the Meta-Game

Abstract: In this paper, we investigate the properties of consistent conjectural variations equilibrium (CCVE) developed for a single-commodity oligopoly. Although, in general, the consistent conjectures are distinct from those of Cournot-Nash, we establish the following remarkable fact. Define a meta-game as such where the players are the same agents as in the original oligopoly but now using the conjectures as their strategies. Then the consistent conjectures of the original oligopoly game provide for the Cournot-Nash optimal strategies for the meta-game.

Consistent conjectures are optimal Cournot-Nash strategies in the meta-game

Abstract: In this paper, we investigate the properties of consistent conjectural variations equilibrium developed for a single-commodity oligopoly. Although, in general, the consistent conjectures are distinct from those of Cournot-Nash, we establish the following remarkable fact. Define a meta-game as such where the players are the same agents as in the original oligopoly but now using the conjectures as their strategies. Then the consistent conjectures of the original oligopoly game provide for the Cournot-Nash optimal strategies in the meta-game.