Estimating Dynamic Models of Imperfect Competition

We describe a two-step algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov Perfect Equilibrium. In the first step, the policy functions and the law of motion for the state variables are estimated. In the second step, the remaining structural parameters are estimated using the optimality conditions for equilibrium. The second step estimator is a simple simulated minimum distance estimator. The algorithm applies to a broad class of models, including I.O. models with both discrete and continuous controls such as the Ericson and Pakes (1995) model. We test the algorithm on a class of dynamic discrete choice models with normally distributed errors, and a class of dynamic oligopoly models similar to that of Pakes and McGuire (1994).

Dynamic Price Competition with Price Adjustment Costs and Product Differentiation

We study a discrete time dynamic game of price competition with spatially differentiated products and price adjustment costs. We characterise the Markov perfect and the open-loop equilibrium of our game. We find that in the steady state Markov perfect equilibrium, given the presence of adjustment costs, equilibrium prices are always higher than prices at the repeated static Nash solution, even though, adjustment costs are not paid in steady state. This is due to intertemporal strategic complementarity in the strategies of the firms and from the fact that the cost of adjusting prices adds credibility to high price equilibrium strategies. On the other hand, the stationary open-loop equilibrium coincides always with the static solution. Furthermore, in contrast to continuous time games, we show that the stationary Markov perfect equilibrium converges to the static Nash equilibrium when adjustment costs tend to zero. Moreover, we obtain the same convergence result when adjustment costs tend to infinity.Price adjustment costs, Difference game, Markov perfect equilibrium, Open-loop equilibrium

Cores of Cooperative Games in Information Theory

Cores of cooperative games are ubiquitous in information theory, and arise most frequently in the characterization of fundamental limits in various scenarios involving multiple users. Examples include classical settings in network information theory such as Slepian-Wolf source coding and multiple access channels, classical settings in statistics such as robust hypothesis testing, and new settings at the intersection of networking and statistics such as distributed estimation problems for sensor networks. Cooperative game theory allows one to understand aspects of all of these problems from a fresh and unifying perspective that treats users as players in a game, sometimes leading to new insights. At the heart of these analyses are fundamental dualities that have been long studied in the context of cooperative games; for information theoretic purposes, these are dualities between information inequalities on the one hand and properties of rate, capacity or other resource allocation regions on the other.Comment: 12 pages, published at http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/318704 in EURASIP Journal on Wireless Communications and Networking, Special Issue on "Theory and Applications in Multiuser/Multiterminal Communications", April 200

Using a Laplace approximation to estimate the random coefficients logit model by non-linear least squares

Current methods of estimating the random coefficients logit model employ simulations of the distribution of the taste parameters through pseudo-random sequences. These methods suffer from difficulties in estimating correlations between parameters and computational limitations such as the curse of dimensionality. This paper provides a solution to these problems by approximating the integral expression of the expected choice probability using a multivariate extension of the Laplace approximation. Simulation results reveal that our method performs very well, both in terms of accuracy and computational time. This paper is a revised version of CWP01/06.

Comparing Individual-Specific Benefit Estimates for Public Goods: Finite Versus Continuous Mixing in Logit Models

Multi-attribute stated preference data, derived through choice experiments, is used to investigate the consequence of a finite number of preference groups in a sample of Yorkshire Water residential customers on the conditional distributions of willingness to pay in the sample. The research focuses on ‘public good’ values, and retrieves the implicit customer specific welfare measures conditional on a sequence of four observed choices. We assess and contrast the sample evidence for the presence of a finite number of 2, 3, 4 and 5 latent preference groups (classes), and contrast these with the presence of a continuous distribution of parameter estimates using mixed logit models. The main focus is the conditional valuations in the form of marginal values for the consequence of waste water handling and treatment, namely: river water quality, area flooding by sewage, presence of odour and flies, and other water related amenities.Choice experiments, Mixed logit, Latent classes, Individual-specific estimates, Non-market valuation

Estimating a War of Attrition: The Case of the U.S. Movie Theater Industry

This paper provides a tractable empirical framework to analyze firm behavior in a dynamic oligopoly when demand is declining over time. I modify Fudenberg and Tirole (1986).s model of exit in a duopoly with incomplete information to a model that can be used in an oligopoly, and combine this with an auxiliary entry model to address the initial conditions problem. I estimate this model with panel data on the U.S. movie theater industry from 1949 to 1955, using variations in TV diffusion rates across households, market structure before the exit game starts, and other market characteristics to identify the parameters in the theater’s payoff function and the distribution of unobservable fixed costs. Using the estimated model, I measure strategic delays in the exit process due to oligopolistic competition and incomplete information. The delay in exit that arises from strategic interaction is 2.7 years on average. Out of these years, 3.7% of this delay is accounted for by incomplete information, while the remaining 96.3% is explained by oligopolistic competition

Semiparametric Estimation of Markov Decision Processeswith Continuous State Space

We propose a general two-step estimation method for the structural parameters ofpopular semiparametric Markovian discrete choice models that include a class ofMarkovian Games andallow for continuous observable state space. The estimation procedure is simpleas it directly generalizes the computationally attractive methodology of Pesendorferand Schmidt-Dengler (2008) that assumed finite observable states. This extensionis non-trivial as the value functions, to be estimated nonparametrically in the firststage, are defined recursively in a non-linear functional equation. Utilizingstructural assumptions, we show how to consistently estimate the infinitedimensional parameters as the solution to some type II integral equations, thesolving of which is a well-posed problem. We provide sufficient set of primitives toobtain root-T consistent estimators for the finite dimensional structural parametersand the distribution theory for the value functions in a time series framework.Discrete Markov Decision Models, Kernel Smoothing, Markovian Games, Semi-parametric Estimation, Well-Posed Inverse Problem.D