Calculation of an approximate solution of the infinite time-varying LQ-problem

Linear Programming;Algorithm;Optimal Control;operations research

Admissible target paths in economic models

Social Psychology;econometrics

Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games

We survey some recent research results in the field of dynamic cooperative differential games with non-transferable utilities. Problems which fit into this framework occur for instance if a person has more than one objective he likes to optimize or if several persons decide to combine efforts in trying to realize their individual goals. We assume that all persons act in a dynamic environment and that no side-payments take place. For these kind of problems the notion of Pareto efficiency plays a fundamental role. In economic terms, an allocation in which no one can be made better-off without someone else becoming worseoff is called Pareto efficient. In this paper we present as well necessary as sufficient conditions for existence of a Pareto optimum for general non-convex games. These results are elaborated for the special case that the environment can be modeled by a set of linear differential equations and the objectives can be modeled as functions containing just affine quadratic terms. Furthermore we will consider for these games the convex case. In general there exists a continuum of Pareto solutions and the question arises which of these solutions will be chosen by the participating persons. We will flash some ideas from the axiomatic theory of bargaining, which was initiated by Nash [16, 17], to predict the compromise the persons will reach.Dynamic Optimization;Pareto Efficiency;Cooperative Differential Games;LQ The- ory;Riccati Equations;Bargaining

Algorithms for Computing Nash Equilibria in Deterministic LQ Games

In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.Algebraic Riccati equations;linear quadratic differential games;Nash equilibria

On the Matrix (I + X)-1

In this note we consider the question under which conditions all entries of the matrix I-(I+X)-1 are nonnegative in case matrix X is a real positive definite matrix.Sufficient conditions are presented as well as some necessary conditions.One sufficient condition is that matrix X-1 is an inverse M-matrix.A class of matrices for which the inequality holds is presented.matrices

On the existence of a positive definite solution of the matrix equation X+AXA=I

Matrices;mathematics

Local strong D-Monotonicity of the Kalai-Smorodinsky and Nash bargaining solution

bargaining

Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.linear-quadratic games;linear feedback Nash equilibrium;affine systems;solvability conditions;Riccati equations