Generalisations of Quasi-Hyperbolic Discounting

<p>This paper proposes several time preference specifications that generalise quasi-hyperbolic discounting, while retaining its analytical tractability. We define their discount functions and provide a recursive formulation of the implied lifetime payoffs. A calibration exercise demonstrates that these specifications deliver better approximations to true hyperbolic discounting. We characterise the Markov-perfect equilibrium of a general intra-personal game of agents with various time preferences. When applied to specific economic examples, our proposals yield policies that are close to those of true hyperbolic discounters. Furthermore, these approximations can be used in settings where an exact solution for hyperbolic agents is not available. Finally, we suggest further generalisations which would provide an even better fit.</p>

Generalisations of Quasi-Hyperbolic Discounting

<p>This paper proposes several time preference specifications that generalise quasi-hyperbolic discounting, while retaining its analytical tractability. We define their discount functions and provide a recursive formulation of the implied lifetime payoffs. A calibration exercise demonstrates that these specifications deliver better approximations to true hyperbolic discounting. We characterise the Markov-perfect equilibrium of a general intra-personal game of agents with various time preferences. When applied to specific economic examples, our proposals yield policies that are close to those of true hyperbolic discounters. Furthermore, these approximations can be used in settings where an exact solution for hyperbolic agents is not available. Finally, we suggest further generalisations which would provide an even better fit.</p>

A novel recursive formulation for dynamic modeling and trajectory tracking control of multi-rigid-link robotic manipulators mounted on a mobile platform

This article establishes an innovative and general approach for the dynamic modeling and trajectory tracking control of a serial robotic manipulator with n-rigid links connected by revolute joints and mounted on an autonomous wheeled mobile platform. To this end, first the Gibbs–Appell formulation is applied to derive the motion equations of the mentioned robotic system in closed form. In fact, by using this dynamic method, one can eliminate the disadvantage of dealing with the Lagrange Multipliers that arise from nonholonomic system constraints. Then, based on a predictive control approach, a general recursive formulation is used to analytically obtain the kinematic control laws. This multivariable kinematic controller determines the desired values of linear and angular velocities for the mobile base and manipulator arms by minimizing a point-wise quadratic cost function for the predicted tracking errors between the current position and the reference trajectory of the system. Again, by relying on predictive control, the dynamic model of the system in state space form and the desired velocities obtained from the kinematic controller are exploited to find proper input control torques for the robotic mechanism in the presence of model uncertainties. Finally, a computer simulation is performed to demonstrate that the proposed algorithm can dynamically model and simultaneously control the trajectories of the mobile base and the end-effector of such a complicated and high-degree-of-freedom robotic system.

Recursive Contracts

We obtain a recursive formulation for a general class of optimization problems with forward‐looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle‐point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner's problem. The recursive formulation is obtained after adding a co‐state variable μ t summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with μ t playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems.