A User''s Guide to Solving Dynamic Stochastic Games Using the Homotopy Method

This paper provides a step-by-step guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its implementation and present two detailed examples of dynamic stochastic games that are solved using this method.

Learning-by-Doing, Organizational Forgetting, and Industry Dynamics

Learning-by-doing and organizational forgetting have been shown to be important in a variety of industrial settings. This paper provides a general model of dynamic competition that accounts for these economic fundamentals and shows how they shape industry structure and dynamics. Previously obtained results regarding the dominance properties of firms' pricing behavior no longer hold in this more general setting. We show that forgetting does not simply negate learning. Rather, learning and forgetting are distinct economic forces. In particular, a model with learning and forgetting can give rise to aggressive pricing behavior, market dominance, and multiple equilibria, whereas a model with learning alone cannot.

Is Dynamic Competition Socially Beneficial? The Case of Price as Investment

We study industries where prices are not limited to their allocative and distributive roles, but also serve as an investment into lower costs or higher demand. While our model focuses on learning-by-doing and the cost advantage that it implies, our conclusions also apply to industries driven by network externalities. Existing literature does not have a clear verdict on whether the investment role of prices benefits or hurts the overall welfare, as there are a number of economic forces at work, e.g. motivation to move down the learning curve faster could be offset by the ease of driving a weaker rival out of the market. We compute both market equilibrium and first-best solution. The resulting deadweight loss appears small, in the sense that eliminating the investment motive from pricing decisions leads to much worse outcomes. Further investigation into components of deadweight loss shows that while pricing distortions are the most important driver of the deadweight loss, these distortions can be fairly small. Entry-exit distortions that arise from duplicated set-up and fixed opportunity costs also contribute to the deadweight loss, but these distortions are partially offset by more beneficial industry structure, as the market equilibrium tends to result in more active firms than the first-best solution

The Economics of Predation: What Drives Pricing When There is Learning-by-Doing?

We formally characterize predatory pricing in a modern industry-dynamics framework that endogenizes competitive advantage and industry structure. As an illustrative example we focus on learning-by-doing. To disentangle predatory pricing from mere competition for efficiency on a learning curve we decompose the equilibrium pricing condition. We show that forcing firms to ignore the predatory incentives in setting their prices can have a large impact and that this impact stems from eliminating equilibria with predation-like behavior. Along with predation-like behavior, however, a fair amount of competition for the market is eliminated

An Optimal Control Model of Technology Transition

This paper discusses the use of optimization software to solve an optimal control problem arising in the modeling of technology transition. We set up a series of increasingly complex models with such features as learning-by-doing, adjustment cost, and capital investment. The models are written in continuous time and then discretized by using different methods to transform them into large-scale nonlinear programs. We use a modeling language and numerical optimization methods to solve the optimization problem. Our results are consistent with ndings in the literature and highlight the impact the discretization choice has on the solution and accuracy.

A User\u27s Guide to Solving Dynamic Stochastic Games Using the Homotopy Method

This paper provides a step-by-step guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its implementation and present two detailed examples of dynamic stochastic games that are solved using this method

Learning-by-Doing, Organizational Forgetting, and Industry Dynamics

Learning-by-doing and organizational forgetting are empirically important in a variety of industrial settings. This paper provides a general model of dynamic competition that accounts for these fundamentals and shows how they shape industry structure and dynamics. We show that forgetting does not simply negate learning. Rather, they are distinct economic forces that interact in subtle ways to produce a great variety of pricing behaviors and industry dynamics. In particular, a model with learning and forgetting can give rise to aggressive pricing behavior, varying degrees of long-run industry concentration ranging from moderate leadership to absolute dominance, and multiple equilibria

Dynamic R&D and the Effectiveness of Policy Intervention in the Pharmaceutical Industry

This study structurally estimates a dynamic model of drug development process in pharmaceutical industry, and uses counterfactual experiments to evaluate effects of various policy interventions aimed at increasing the introduction rate of new drugs within a specifi…c therapeutic area. Advanced computational methods --such as continuous time and polynomial approximations --overcome the modeling difficulties that limited previous studies to one or two stages of development process, and allow the model to describe the progress of drugs through all three phases of clinical trials and FDA approval. The primary result is that most policies affecting earlier stages of drug development are less effective than those aimed at later stages. The reason for this …finding is a strategic response to policy-induced changes in the number of drugs under development and on the market