We examine an oligopoly model of advertising competition where each firm's market share depends on its own and its competitors' advertising decisions. A differential game model is developed and used to derive the closed-loop Nash equilibrium under symmetric as well as asymmetric competition. We...

We develop a general methodology for a partially observed stochastic control problem. The dynamics is governed by a discrete-time Markov process. We describe an application to an inventory system with possibility of shrinkage, and introduce unnormalized conditional probabilities to transform the...

In this paper, the problem of machine replacement in a changing technological environment is formulated as a problem in modern control theory. The objective is to maximize the present value of all future net profits over a class of infinite chains of machines where each link in the chain...

Linear optimal control problems with state inequality constraints is an important class of large systems. This paper shows that a generalized programming formulation of these problems does not result in a decomposition over time or a maximum principle as it does for problems without the state...

In this paper, we identify a new class of stochastic Iinear convex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term 'linear convex' is meant to imply that the dynamics is linear and the cost function is...

This paper derives a maximum principle for dynamic systems with continuous lags, i.e., systems governed by integrodifferential equations, using dynamic programming. As a result, the adjoint variables can be provided with useful economic interpretations

We consider a finite-horizon control model with additive input. There are two convex functions which describe the running cost and the terminal cost within the system. The cost of input is proportional to the input and can take both positive and negative values. It is shown that there exists a...

In this paper, we analyze the optimal skill mix in a model with two kinds of imperfectly substitutable labor, skilled and unskilled. The population is characterized by a distribution of innate abilities, and individuals are trained according to optimal rules or market rules (with imperfect...