This papers shows that complex dynamics arise naturally in deterministic discrete choice problems. In particular, we show that if the objective function of a maximization problem can be written as a function of a sequence of discrete variables, and if the (maximized) value function is strictly...

We show that the critical capital stock of the Dechert-Nishimura (1983) model is a decreasing and continuous function of the discount factor. We also show that the critical capital stock merges with a nonzero steady state as the discount factor decreases to a certain boundary value, and that the...

We study existence and uniqueness of a fixed point for the Bellman operator in deterministic dynamic programming. We show that removing many of the assumptions of the theorem on the Bellman operator recently shown by Martins-da-Rocha and Vailakis ("Existence and Uniqueness of a Fixed Point for...

This paper strengthens the Hopenhayn and Prescott stability theorem for monotone economies. We extend the theorem to a larger class of applications, and develop new perspectives on the nature and causes of stability and instability. In addition, we show that models satisfying the...

We analyze an infinitely repeated tariff-setting game played by two large countries with alternating moves. We focus on the subgame perfect equilibria in which each country chooses its tariff according to a stationary function of the other country's tariff. We show that there are many equilibria...

We discuss 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 distribution,...

This paper generalizes the sufficient conditions for stability of monotone economies and time series models due to Hopenhayn and Prescott (Econometrica, 60, p. 1387–1406, 1992). We introduce a new order-theoretic mixing condition and characterize stability for monotone economies satisfying...

We study rational bubbles in a standard linear asset price model. We first consider a class of bubble processes driven by multiplicative iid shocks. We show that a bubble process in this class either diverges to infinity with probability one, converges to zero with probability one, or keeps...

We analyze a infinitely repeated tariff-setting game by two large countries with alternating moves. We focus on the subgame perfect equilibria in which each country chooses its tariff according to a stationary function of the other country's tariff. We show that there are many equilibria with...

Production takes time, and labor supply and profit maximization decisions that relate to current production are typically made before all shocks affecting that production have been realized. In this paper we re-examine the problem of stochastic optimal growth with aggregate risk where the timing...