1,721,028 research outputs found
A Note on Open Loop Nash Equilibrium in Linear-State Differential Games
Full text linkIn this paper we focus on non-cooperative two-player linear-state differential games. In the standard definition this family is introduced assuming that there is no multiplicative interaction among state and control variables. In this paper we show that a multiplicative interaction between the state and the control of one player does not destroy the analytical features of the linear-state differential games if it appears in the objective functional of the other player. We prove that this slightly new definition preserves not only the solvability of the differential game, but also the subgame perfectness of an Open Loop Nash Equilibrium
Advertising for a new product introduction: a stochastic approach
Full text linkMany marketing policies can be correctly explained and analyzed only through a stochastic approach to the problem. In this thesis the planning of a pre-launch publicity campaign has been studied using the stochastic control theory and some recent results of the stochastic linear quadratic control theory. We assume that a firm controls the goodwill evolution of a product through the advertising flow, or some other communication channel, in the programming interval [0, T]. The advertising flow increases the goodwill level which otherwise spontaneously decreases. Such hypotheses have been introduced by Nerlove and Arrow in a deterministic framework and have led to the development of a model class called “advertising capital model , in which the advertising flow is considered as an investment in goodwill (a stock
which represents the firm image in the market). In this work:
• we assume that the advertising effects on the goodwill evolution are stochastic;
• we describe the effects of the word-of-mouth publicity, by introducing a diffusion term representing the goodwill volatility;
• we assume that the firm can use different advertising channels
Linear State Optimal Control Problem with a Stochastic Switching Time
Full text linkIn this paper, we analyse an optimal control problem over a finite horizon with a stochastic switching time, assuming that the two optimal control problems present in its two stages have a particularly simple form called linear state. It is well known that linear state optimal control problems can be solved easily using the HJB equation approach and assuming that the value function is linear in the state. Unfortunately, this simplicity of solution does not extend to the problem with stochastic switching time. We prove that a necessary and sufficient condition for the problem to maintain a linear state structure is to assume that the hazard rate of the switching time depends only on the temporal variable. Finally, assuming that the hazard rate is constant, we completely characterise the solution of the obtained linear state optimal control problem
Brand Extension Using a Licensing Contract with Uncertainty Advertising Effects
No full textA licensing contract is studied as a Stackelberg differential game with the licensor as the leader and the licensee as the follower. We assume that both players can advertise to increase the brand value, but licensee’s advertising introduces an uncertainty effect in the brand evolution.
The objective of the licensee is to maximize her expected profit, while the objective of the licensor is twofold. He wants to maximize his expected profit and at the same time he wants to extend the value of his brand. If the advertising campaign planned at the beginning of the programming
interval is required to be open-loop and deterministic, then
the stochastic differential game becomes deterministic. We take into account brand extension by mean of two approaches. In the first one we require the mean brand value to be greater than a given threshold, in the second one we require that the final constraint is satisfied with a given probability. We characterize the deterministic optimal strategies for both players and analyze the economic meaning of the obtained results
Reciprocal optimal control problems and the associated Pareto frontier
No full textIt is well known that, if a control is Pareto optimal for a multiobjective optimal control problem, then it satisfies the necessary conditions of an optimal control problem with isoperimetric constraints. We introduce a set of sufficient conditions reversing that implication. Thus, we study some properties of the isoperimetric problems and their applications to the analysis of economic models
Advertising in a segmented market: comparison of media choices
Full text linkSegmentation is a core strategy in modern marketing but, to the best of our knowledge, it is not considered in most dynamic advertising models. In this paper, we aim to fill such a gap by presenting a dynamic advertising model which includes market segmentation. First, we model goodwill evolution in a segmented market under the assumption that the decision maker may independently choose the advertising intensity directed at each different segment. Then, we assume that the decision maker must use a single medium, which reaches several segments with different effectiveness. We obtain the explicit solutions of the relevant optimal control problems. These results permit us to compare the two different contexts and to obtain a preference index for advertising media
Minimum time problems in Economics
No full textWe analyze the connection between the optimal solutions of minimum time and fixed final time optimal control problems. We discuss some controllability conditions which guarantee the equivalence of the two problems. In fact, under such conditions, not only does an optimal control maximize/minimize the objective functional, but it does it in minimum time too. We apply the results to some Economics models in order to obtain a deeper understanding of the optimal solutions of the related control problems
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