We propose an approximation method for analyzing Ericson and Pakes (1995)-style dynamic models of imperfect competition. We develop a simple algorithm for computing an ``oblivious equilibrium,'' in which each firm is assumed to make decisions based only on its own state and knowledge of the long run average industry state, but where firms ignore current information about competitors' states. We prove that, as the market becomes large, if the equilibrium distribution of firm states obeys a certain ``light-tail'' condition, then oblivious equilibria closely approximate Markov perfect equilibria. We develop bounds that can be computed to assess the accuracy of the approximation for any given applied problem. Through computational experiments, we find that the method often generates useful approximations for industries with hundreds of firms and in some cases even tens of firms.

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 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. * The authors are grateful for helpful conversations with

We propose an approximation method for analyzing Ericson and Pakes (1995)-style dynamic models of imperfect competition. We develop a simple algorithm for computing an ``oblivious equilibrium,'' in which each firm is assumed to make decisions based only on its own state and knowledge of the long run average industry state, but where firms ignore current information about competitors' states. We prove that, as the market becomes large, if the equilibrium distribution of firm states obeys a certain ``light-tail'' condition, then oblivious equilibria closely approximate Markov perfect equilibria. We develop bounds that can be computed to assess the accuracy of the approximation for any given applied problem. Through computational experiments, we find that the method often generates useful approximations for industries with hundreds of firms and in some cases even tens of firms.

A d exchanges are emerging Internet markets where advertisers may purchase display ad placements, in real time and based on specific viewer information, directly from publishers via a simple auction mechanism. Advertisers join these markets with a prespecified budget and participate in multiple second-price auctions over the length of a campaign. This paper studies the competitive landscape that arises in ad exchanges and the implications for publishers' decisions. The presence of budgets introduces dynamic interactions among advertisers that need to be taken into account when attempting to characterize the bidding landscape or the impact of changes in the auction design. To this end, we introduce the notion of a fluid mean-field equilibrium (FMFE) that is behaviorally appealing and computationally tractable, and in some important cases, it yields a closed-form characterization. We establish that an FMFE approximates well the rational behavior of advertisers in these markets. We then show how this framework may be used to provide sharp prescriptions for key auction design decisions that publishers face in these markets. In particular, we show that ignoring budgets, a common practice in this literature, can result in significant profit losses for the publisher when setting the reserve price.

We analyze investment incentives and market structure under oligopoly competition in industries with congestion effects. Our results are particularly focused on models inspired by modern technology-based services such as telecommunications and computing services. We consider situations where firms compete by simultaneously choosing prices and investments; increasing investment reduces the congestion disutility experienced by consumers. We define a notion of returns to investment, according to which congestion models inspired by delay exhibit increasing returns, whereas loss models exhibit nonincreasing returns. For a broad range of models with nonincreasing returns to investment, we characterize and establish uniqueness of pure-strategy Nash equilibrium. We also provide conditions for existence of pure-strategy Nash equilibrium. We extend our analysis to a model in which firms must additionally decide whether to enter the industry. Our theoretical results contribute to the basic understanding of competition in service industries and yield insight into business and policy considerations.