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>

On a special case of non-symmetric resource extraction games with unbounded payoffs

The game of resource extraction/capital accumulation is a stochastic infinite-horizon game, which models a joint utilization of a productive asset over time. The paper complements the available results on pure Markov perfect equilibrium existence in the non-symmetric game setting with an arbitrary number of agents. Moreover, we allow that the players have unbounded utilities and relax the assumption that the stochastic kernels of the transition probability must depend only on the amount of resource before consumption. This class of the game has not been examined beforehand. However, we could prove the Markov perfect equilibrium existence only in the specific case of interest. Namely, when the players have constant relative risk aversion (CRRA) power utilities and the transition law follows a geometric random walk in relation to the joint investment. The setup with the chosen characteristics is motivated by economic considerations, which makes it relevant to a certain range of real-word problems.

Revenue Management without Commitment: Dynamic Pricing and Periodic Flash Sales

A seller has a fixed number of goods to sell by a deadline. At each time, he posts a regular price and decides whether to hold a flash sale. Over time, buyers privately enter the market and strategically time their purchases. If a buyer does not purchase when she arrives, she can pay an attention cost to recheck the regular price afterwards, or she can wait for future flash sales where she may obtain a good at a discounted price. In the unique Markov perfect equilibrium, the seller sporadically holds flash sales to lower the stock of goods. A flash sale increases the willingness to pay of future buyers, but decreases the willingness to pay of buyers who arrive early in the game. When it is very likely that a buyer will obtain a good in a flash sale, the seller holds a “big” initial flash sale for all but one unit of the good.

The Dynamics of Disease in a Regulated Vertically Differentiated Health System

We build up a differential game to investigate the interplay between the quality of health care and the presence of an evolving disease in a duopoly where patients are heterogeneous along the income dimension. We study the Markov perfect equilibrium, and we identify the admissible parameter region wherein price regulation achieves the twofold objectives of ensuring cares to all patients and heal all of them.

DEBT AND DEFICIT FLUCTUATIONS IN A TIME-CONSISTENT SETUP

This paper compares the stochastic behavior of fiscal variables under optimal fiscal policy for the cases of full commitment by the government (Ramsey problem) and no commitment by the government (focusing on differentiable Markov perfect equilibrium). It shows that the cyclical properties of fiscal variables are similar for both commitment assumptions. These conclusions are robust to two different specifications of the structure of public bonds (risk-free and state-contingent) and to different sets of the parameters. The cyclical properties of fiscal variables, regardless of commitment assumptions, can be determined by the parameters of the utility function.