Dynamic Games with Asymmetric Information: A Framework for Empirical Work


August 29, 2012


We develop a framework for the analysis of dynamic games that can be applied to the analysis of firm which compete in a market whose characteristics evolve over time as a probabilistic function of the actions of the firms competing in that market. Firm’s chose their actions to maximize their perceptions of the discounted value of the returns that will accrue to them as a result of those actions. These returns depend on both their own states and their competitor’s states. The firms know their own states, but only observe imprecise signals on the states of their competitors. Our goal is to provide a framework capable of analyzing the impact of policy or environmental changes in such a setting. Bayesian perfect Nash equilibria for environments that are rich enough to adequately approximate behavior have computational and informational demands that both; (i) make them impossible for applied researchers to use, and (ii) unlikely to be the best approximation to agent’s actual behavior. So we introduce an alternative notion of equilibria which is less demanding of both agents and researchers, while still implying agents “optimize” in a meaningful sense of that word. We show that: (i) there is an artificial intelligence algorithm that makes it relatively easy to compute (at least some of) the resultant equilibria, and (ii) it is relatively easy to use the properties of that equilibria to estimate any unknown parameters of the game. We use the analysis of a de-regulated electric utility market as an example. Two firms each own several generators and bid “supply functions” into the market in every period (a quantity supplied as an increasing function of price). An independent system operator (an ISO) sums the supply curves horizontally and intersects the result with demand to determine the period’s price and the quantities to be produced by each firm. The firm’s cost of supplying electricity on each of its generators is increasing in the current quantity produced and stochastically increasing in the quantities produced since the last time the firm did maintenance on that generator. Firms do not know the current cost of their competitor’s generators but realize that the returns they will earn from the bid on each of its generator will increase the less the quantity supplied by other generators (their own, as well as those of its competitors). This provides incentives for firms to simply shut down some generators without doing maintenance, and to implicitly co-ordinate shutdowns across firms. Consumers pay the price through the resultant increase in the price of electricity.

Joint work with Chaim Fershtman


Ariel Pakes

Ariel Pakes is the Steven McArthur Heller Professor of Economics in the Department of Economics at Harvard University, where he teaches courses in Industrial Organization and in Econometrics. Before coming to Harvard in 1999, he was the Charles and Dorothea Dilley Professor of Economics at Yale University (1997-99). He has held other tenured positions at Yale (1988-97), the University of Wisconsin (1986-88), and the University of Jerusalem (1985-86). Pakes received his doctorate degree from Harvard University in 1980, and he stayed at Harvard as a Lecturer until he took up a position in Jerusalem in 1981. Pakes received the award for the best graduate student advisor at Yale in 1996. Pakes was elected fellow of the American Academy of Arts and Sciences in 2002. He received the Frisch Medal of the Econometric Society in 1986, was elected as a fellow of that society in 1988, and gave the Fisher-Schultz lecture at the World Congress of that society in 2005. He was the Distinguished Fellow of the Industrial Organization Society in 2007. He has been on the editorial boards of the RAND Journal of Economics, Econometrica, Economic Letters and the Journal of Economic Dynamics and Control. He is also a research associate of the NBER, and has been member of the AEA Committee on Government Statistics, the chair of the AEA Census Advisory Panel, and co-editor of a Proceedings of the National Academy of Science issue on “Science, Technology and the Economy”. Professor Pakes’ research has been in Industrial Organization (I.O.), the Economics of Technological Change and in Econometric Theory. He and his co-authors have focused on developing techniques which allow us to analyze market responses to policy and environmental changes. This includes; econometric work on how to estimate demand and cost systems and then use the estimated parameters to analyze equilibrium responses in different institutional settings, empirical work which uses these techniques to analyze market outcomes in different industries, and theoretical work developing frameworks for the applied analysis of dynamic oligopolies (with and without collusive possibilities, and with and without asymmetric information).