Knowledge that Transforms

Reinforcement learning and stochastic fictitious play are apparent rivals as models of human learning. They embody quite different assumptions about the processing of information and optimization. This paper compares their properties and finds that they are far more similar than were thought. In particular, the expected motion of stochastic fictitious play and reinforcement learning with experimentation can both be written as a perturbed form of the evolutionary replicator dynamics. Therefore they will in many cases have the same asymptotic behavior. In particular, local stability of mixed equilibria under stochastic fictitious play implies local stability under perturbed reinforcement learning. The main identifiable difference between the two models is speed: stochastic fictitious play gives rise to faster learning. Copyright The Econometric Society 2002.

Choice models with nonlinear budget sets are important in econometrics.In this paper we propose a nonparametric approach to estimation of choice models with nonlinear budget sets.The basic idea is to think of the choice, in our case hours of labor supply, as being a function of the entire budget set.Then we can ac- count nonparametrically for a nonlinear budget set by estimating a nonparametric regression where the variable in the regression is the budget set.We reduce the dimensionality of this problem by exploiting additive structure implied by utility maximization with convex budget sets.This structure leads to a polynomial con- vergence rate for the estimator.We give asymptotic normality results also.The usefulness of the estimator is demonstrated in Monte Carlo and empirical work, where we find it can have a large impact on estimated effects of tax changes.

The goal of this paper is to probe the validity of the fiscal theory of the price level by modeling explicitly the market structure in which households and the governments make their decisions. I describe the economy as a game, and I am thus able to state precisely the consequences of actions that are out of the equilibrium path. I show that there exist government strategies that lead to a version of the fiscal theory, in which the price level is determined by fiscal variables alone. However, these strategies are more complex than the simple budgetary rules usually associated with the fiscal theory, and the government budget constraint cannot be merely viewed as an equilibrium condition.