This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal pat...

In many Western countries, the relative weight of people -- measured by the body mass index (BMI) -- has increased substantially in recent years, leading to an increasing incidence of overweight and related health problems. As with many forms of risky behavior, it is plausible that overweight is related to the individual discount rate. Increases in credit card debts, the rise in gambling and th...

We study a model of multilateral bargaining over social outcomes represented by points in the unit interval. An acceptance or rejection of a proposal is determined by a voting rule as represented by a collection of decisive coalitions. The focus of the paper is on the asymptotic behavior of subgame perfect equilibria in stationary strategies as the discount factor goes to one. We show that, alo...

We study the links between the values of stochastic games with varying stage duration h, the corresponding Shapley operators T and Th = hT+ (1− h)Id and the solution of the evolution equation ḟt = (T − Id)ft. Considering general non expansive maps we establish two kinds of results, under both the discounted or the finite length framework, that apply to the class of “exact” stochastic games. Fir...

We characterize the compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk. Given an underlying Markov diffusion that governs the state variables in the economy, the economic model implies a stochastic discount factor process S and a reference stochastic growth process G for the macroeconomy. Both are modeled conveniently as multiplicative functionals of ...

A stationary variant of the repeated prisoners’ dilemma in which the game frontier is a parallelogram is analyzed. By using the probabilistic cheap talk concept of [3], the discount factor becomes fungible, and for a critical value of the discount factor a unique Pareto-optimal and Pareto-dominant solution can be found. The relative bargaining power of the players can be quantified in terms of ...

We present a new complexity result on solving the Markov decision problem (MDP) with n states and a number of actions for each state, a special class of realnumber linear programs with the Leontief matrix structure. We prove that, when the discount factor θ is strictly less than 1, the problem can be solved in at most O(n1.5(log 1 1−θ +log n)) classical interior-point method iterations and O(n ...

Using deep neural nets as function approximator for reinforcement learning tasks have recently been shown to be very powerful for solving problems approaching real-world complexity such as [1]. Using these results as a benchmark, we discuss the role that the discount factor may play in the quality of the learning process of a deep Q-network (DQN). When the discount factor progressively increase...