Equilibria of dynamic games with many players: Existence, approximation, and market structure

In this paper we study stochastic dynamic games with many players; these are a fundamental model for a wide range of economic applications. The standard solution concept for such games is Markov perfect equilibrium (MPE), but it is well known that MPE computation becomes intractable as the number of players increases. We instead consider the notion of stationary equilibrium (SE), where players optimize assuming the empirical distribution of others' states remains constant at its long run average. We make two main contributions. First, we provide a rigorous justification for using SE. In particular, we provide a parsimonious collection of exogenous conditions over model primitives that guarantee existence of SE, and ensure that an appropriate approximation property to MPE holds, in a general model with possibly unbounded state spaces. Second, we draw a significant connection between the validity of SE, and market structure: under the same conditions that imply SE exist and approximates MPE well, the market becomes fragmented in the limit of many firms. To illustrate this connection, we study in detail a series of dynamic oligopoly examples. These examples show that our conditions enforce a form of “decreasing returns to larger states;” this yields fragmented industries in the SE limit. By contrast, violation of these conditions suggests “increasing returns to larger states” and potential market concentration. In that sense, our work uses a fully dynamic framework to also contribute to a longstanding issue in industrial organization: understanding the determinants of market structure in different industries

RAND Journal of Economics

approach to solving dynamic oligopoly models Vivek Farias ∗ Denis Saure∗ ∗ and Gabriel Y. Weintraub∗∗ ∗ In this article, we introduce a new method to approximate Markov perfect equilibrium in largescale Ericson and Pakes (1995)-style dynamic oligopoly models that are not amenable to exact solution due to the curse of dimensionality. The method is based on an algorithm that iterates an approximate best response operator using an approximate dynamic programming approach. The method, based on mathematical programming, approximates the value function with a linear combination of basis functions. We provide results that lend theoretical support to our approach. We introduce a rich yet tractable set of basis functions, and test our method on important classes of models. Our results suggest that the approach we propose significantly expands the set of dynamic oligopoly models that can be analyzed computationally. 1

Is something really wrong with macroeconomics?

While there is much that is wrong with macroeconomics today, most critiques of the state of macroeconomics are off target. Current macroeconomic research is not mindless DSGE modeling filled with ridiculous assumptions and oblivious of data. Rather, young macroeconomists are doing vibrant, varied, and exciting work, getting jobs, and being published. Macroeconomics informs economic policy only moderately and not more nor all that differently than other fields in economics. Monetary policy has benefitted significantly from this advice in keeping inflation under control and preventing a new Great Depression. Macroeconomic forecasts perform poorly in absolute terms and given the size of the challenge probably always will. But relative to the level of aggregation, the time horizon, and the amount of funding, they are not so obviously worst than those in other fields. What is most wrong with macroeconomics today is perhaps that there is too little discussion of which models to teach and too little investment in graduate-level textbooks

Recovering the sunk costs of R&D: the moulds industry case

Sunk costs for R&D are an important determinant of the level of innovation in the economy. In this paper I recover them using a Markov equilibrium framework. The contribution is twofold. First, a model of industry dynamics which accounts for selection into R&D, capital accumulation and entry/exit is proposed. The industry state is summarized by an aggregate state with the advantage that it avoids the "curse of dimensionality". Second, the estimated sunk costs of R&D for the Portuguese moulds industry are shown to be important (3.4 million Euros). They become particularly relevant since the industry is mostly populated by small firms. Institutional changes in the early 1990s generated an increase in demand from European car makers and created the incentives for firms to pay the costs of investment. Trade-induced innovation reinforced the selection effect by which international trade leads to productivity growth. Finally, using the estimated parameters, simulations evaluate the effects of changes in market size, sunk costs and entry costs

Recovering the Sunk Costs of R&D: the Moulds Industry Case

Sunk costs for R&D are an important determinant of the level of innovation in the economy. In this paper I recover them using a Markov equilibrium framework. The contribution is twofold. First, a model of industry dynamics which accounts for selection into R&D, capital accumulation and entry/exit is proposed. The industry state is summarized by an aggregate state with the advantage that it avoids the "curse of dimensionality". Second, the estimated sunk costs of R&D for the Portuguese moulds industry are shown to be important (3.4 million Euros). They become particularly relevant since the industry is mostly populated by small firms. Institutional changes in the early 1990s generated an increase in demand from European car makers and created the incentives for firms to pay the costs of investment. Trade-induced innovation reinforced the selection effect by which international trade leads to productivity growth. Finally, using the estimated parameters, simulations evaluate the effects of changes in market size, sunk costs and entry costs.Aggregate state, industry dynamics, Markov equilibrium, moulds industry, R&D, structural estimation, sunk costs

The Political Economy of Globalization – Revisiting Stephen Hymer 50 Years On

We discuss issues pertaining to the political economy of “globalization”, in the context of the seminal contribution by Stephen Hymer. While Hymer’s contribution to the theory of the multinational enterprise (MNE) and foreign direct investment (FDI) is widely recognized, his contribution to the political economy of what he called “multinational corporate capital” has received less attention. In this paper we revisit some of the issues he raised, notably uneven development, global governance and central planning in the context of post-Hymer scholarly thinking and the shifting global landscape. In so doing we also speculate on the challenges and future of globalization.Stephen Hymer, International Political Economy, Institutions, Globalization,Sustainability

An aggregation method for large-scale dynamic games

It is a well known fact that many dynamic games are subject to the curse of dimensionality, limiting the ability to use them in the study of real-world problems. I propose a new method to solve complex large-scale dynamic games using aggregation as an approximate solution. I obtain two fundamental characterization results. First, approximations with small within-state variation in the primitives have a smaller maximum error bound. I provide numerical results which compare the exact errors and the bound. Second, I find that for monotone games, order preserving aggregation is a necessary condition of any optimal aggregation. I suggest using quantiles as a straightforward implementation of an order preserving aggregation architecture for industry distributions. I conclude with an illustration, by solving and estimating a stylized dynamic reputation game for the hotel industry. Simulation results show maximal errors between the exact and approximated solutions below 6%, with average errors below 1%.publishersversionpublishe