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Steady State Learning and Nash Equilibrium

Econometrica 1993 61(3), 547
We study the steady states of a system in which players learn about the strategies their opponents are playing by updating their Bayesian priors in light of their observations.Players are matched at random to play a fixed extensive -form game, and each player observes the realized actions in his own matches, but not the intended off -path play of his opponents or the realized actions in other matches.If lifetimes are long and players are very patient, the steady state distribution of actions approximates those of a Nash equilibrium.

Self-Confirming Equilibrium

Econometrica 1993 61(3), 523
Self-confirming equilibrium differs from Nash equilibrium in allowing players to have incorrect beliefs about how their opponents would play off of the equilibrium path.We provide several examples of ways that self -confirming and Nash equilibria differ.In games with "identified deviators , " all self -confirming equilibrium outcomes can be generated by extensive -form correlated equilibria.In two-player games, self -confirming equilibria with "unitary beliefs" are Nash.1.

Rationing, Queues, and Black Markets

Econometrica 1993 61(1), 1
Several types of rationing and queue mechanisms are compared in a framework of general equilibrium type models under gross substitutability and normality assumptions about consumers' Walrasian demand. During transition from rationing and queues to a market system, a group of low income people loses. The transition involves larger losses for this group if black markets prevail under rationing or queues, while a group of high income consumers gains. Some other comparative statics results are developed for a queue model with black markets. Copyright 1993 by The Econometric Society.

Renegotiation in Finitely Repeated Games

Econometrica 1993 61(2), 303 open access
Perfect equilibria of finitely repeated games may be vulnerable to the possibility of renegotiation among players. We study the limiting properties of the set of payoffs from equilibria that are immune to renegotiation. Our main result is that the limit of the set of payoffs from renegotiation proof equilibria is either a singleton or a connected subset of the Pareto efficient frontier. A simple sufficient condition for the latter to occur is also provided.

Temporal Aggregation of Garch Processes

Econometrica 1993 61(4), 909
The authors derive low frequency, say weekly, models implied by high frequency, say daily, ARMA models with symmetric GARCH errors. They show that low frequency models exhibit conditional heteroskedasticity of the GARCH form as well. The parameters in the conditional variance equation of the low frequency model depend upon mean, variance, and kurtosis parameters of the corresponding high frequency model. Moreover, strongly consistent estimators of the parameters in the high frequency model can be derived from low frequency data. The common assumption in applications that rescaled innovations are independent is disputable, since it depends upon the available data frequency. Copyright 1993 by The Econometric Society.

Making a Miracle

Econometrica 1993 61(2), 251
This lecture surveys recent models of growth and trade in search of descriptions of technologies that are consistent with episodes of very rapid income growth. Emphasis is placed on the on-the-job accumulation of human capital: learning by doing. Possib le connections between learning rates and international trade are discussed Copyright 1993 by The Econometric Society.

The Limiting Distribution of the Maximum Rank Correlation Estimator

Econometrica 1993 61(1), 123
Han’s maximum rank correlation (MRC) estimator is shown to be√ n-consistent and asymptotically normal. The proof rests on a general method for determining the asymptotic distribution of a maximization estimator, a simple U-statistic decomposition, and a uniform bound for degenerate U-processes. A consistent estimator of the asymptotic covari-ance matrix is provided, along with a result giving the explicit form of this matrix for any model within the scope of the MRC estimator. The latter result is applied to the binary choice model, and it is found that the MRC estimator does not achieve the semiparametric efficiency bound.