Strategic interaction and dynamics under endogenous time preference

Abstract

a b s t r a c tThis paper presents a strategic growth model with endogenous time preference. Due to the potential lack of concavity and the differentiability of the value functions associated with each agent's problem, we employ the theory of monotone comparative statics and supermodular games based on order and monotonicity properties on lattices. In particular, we provide the sufficient conditions of supermodularity for dynamic games with open-loop strategies based on two fundamental elements: the ability to order elements in the strategy space of the agents and the strategic complementarity which implies upward sloping best responses. The supermodular game structure of the model lets us provide the existence and the monotonicity results on the greatest and the least equilibria. We sharpen these results by showing the differentiability of the value function and the uniqueness of the best response correspondences almost everywhere and show that the stationary state Nash equilibria tend to be symmetric. Finally, we numerically analyze to what extent the strategic complementarity inherent in agents' strategies can alter the convergence results that could have emerged under a single agent optimal growth model. In particular, we show that the initially rich can pull the poor out of the poverty trap even when sustaining a higher level of steady state capital stock for itself.

Strategic Interaction and Catching Up

“…In this setup, households choose their strategies simultaneously and each household is faced with a single criterion optimization problem constrained by the strategies of the rivals taken as given. In this respect, adopting open-loop strategies reflect the slightest departure from the competitive equilibrium framework as it does not allow for genuine interaction between players during the game (see Sorger, 2008;Camacho et al, 2013). However, even under this small departure from the competitive equilibrium framework, we show that considering the strategic interaction among agents in the economy changes the qualitative properties of the standard Ramsey model drastically.…”

“…In this respect, we show that structurally very simple frameworks may lead to limit cycles thanks to the strategic interaction among agents in the economy. (1984), Figueres et al (1999), Dockner and Nishimura (2005) on capital accumulation games; Espino (2005), Bethmann (2008) on Lucas-Uzawa model; Sorger (2008) on Ramsey conjecture and Camacho, et al (2013) on dynamics.…”

Strategic Growth with Recursive Preferences: Decreasing Marginal Impatience

“…In a close paper to ours, Camacho et al (2013) also analyze a strategic growth model with recursive preferences, in which discount factors are a function of capital held by each agent, but preferences are homogeneous. Output shares are determined by the proportion of aggregate capital that each agent holds.…”