We present a novel model of corruption dynamics in the form of a nonlinear optimal dynamic control problem. It has a tipping point, but one whose origins and character are distinct from that in the classic Schelling (1978) model. The decision maker choosing a level of corruption is the chief or...

How should firms price new products when they do not know the timing, nor the nature of the next competitive entry? To guide managers’ pricing decisions in such contexts, we propose a dynamic pricing model with two types of randomly timed entry, i.e. imitative and innovative. The...

The question of simultaneous dynamic pricing, product and process investment policies is crucial for manufacturing and high-tech industries. This paper models these policies in an optimal control setting. On the supply side, the firm sets prices, product and process investment levels over time....

In [21], Sethi et al. introduced a particular new-product adoption model. They determine optimal advertising and pricing policies of an associated deterministic infinite horizon discounted control problem. Their analysis is based on the fact that the corresponding Hamilton–Jacobi–Bellman...

This paper considers a class of optimal control problems that allows jumps in the state variable. We present the necessary optimality conditions of the Impulse Control Maximum Principle based on the current value formulation. By reviewing the existing impulse control models in the literature, we...

We present a differential game to study how companies can simultaneously license their innovations to other firms when launching a new product. The licensee may cannibalize licensor’s sales, albeit this can be compensated by gains from royalties. Nonetheless, patent royalties are generally so...