We establish some elementary results on solutions to the Bellman equation without introducing any topological assumption. Under a small number of conditions, we show that the Bellman equation has a unique solution in a certain set, that this solution is the value function, and that the value...

In this paper we introduce a technique for perfect simulation from the stationary distribution of a standard model of industry dynamics. The method can be adapted to other, possibly non-monotone, regenerative processes found in industrial organization and other fields of economics. The algorithm...

We discuss the stability of discrete-time Markov chains satisfying monotonicity and an order-theoretic mixing condition that can be seen as an alternative to irreducibility. A chain satisfying these conditions has at most one stationary distribution. Moreover, if there is a stationary...