Market Power, Resource Extraction and Pollution: Some Paradoxes and a Unified View

We adopt a stepwise approach to the analysis of a dynamic oligopoly game in which production makes use of a natural resource and pollutes the environment, starting with simple models where firms' output is not a function of the natural resource to end up with a full-fledged model in which (i) the resource is explicitly considered as an input of production and (ii) the natural resource and pollution interact via the respective state equations. This allows us to show that the relationship between the welfare properties of the economic system and the intensity of competition is sensitive to the degree of accuracy with which the model is constructed.

Avoidance control

Dynamical systems were considered, subject to control by two agents, one of whom desires that no trajectory of the system, emanating from outside a given set, intersects the set no matter what the admissible actions of the other agent. Conditions are given whose satisfaction assures that a given control results in avoidance. Furthermore, these conditions are constructive in that they yield an avoidance feedback control. Some examples are presented

Evasion in the plane

Dynamic systems were considered subject to control by two agents, one of whom desires that no trajectory of the system emanating from outside a given set, intersects that set no matter what the admissible actions of the other agent. Constructive conditions sufficient to yield a feedback control for the agent seeking avoidance were employed to deduce an evader control for the planar pursuit-evasion problem with bounded normal accelerations

Qualitative differential games with two targets

So-called differential games of kind (qualitative games) were considered involving two or more players each of whom possesses a target toward which he wished to steer the response of a dynamical system that was under the control of all players. Sufficient conditions were derived, which assure termination on a particular player's target. In general, these conditions were constructive in that they permited construction of a winning (terminating) strategy for a player. The theory is illustrated by a pursuit-evasion problem

On One Aspect of Science Policy Based on an Uncertain Model

We discuss one aspect of the allocation of new scientists to teaching and research careers. In the past, this allocation problem was treated on the basis of a model with known constant parameters and as a classical open-loop optimal control problem with the allocation ratio as the sole control variable. The utility function in that treatment took both short term and long term goals into account. Here we allow for uncertainty in the possibly time-varying system parameters, and we account for the possibility of new scientists going into careers other than teaching and research. We treat the allocation problem not as an optimal control one but rather as one robust control, insensitive to uncertainties, in order to assure desired numbers of teachers and scientists within a computable horizon

Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions. Leitmann's avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.Comment: Revised edition in JOTA format. To appear in J. Optim. Theory Appl. 145 (2010), no. 3. In Pres

The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

Hahn's Symmetric Quantum Variational Calculus

We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for variational problems within the context of Hahn's symmetric calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric variational calculus. Illustrative examples are provided.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 06-Sept-201

A Stochastic Optimal Control Model of Pollution Abatement

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