Knowledge that Transforms

We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stochastic process to the limit behavior of a differential equation defined by the expected motion of the process. The key result in our analysis of supermodular games is that the relevant differential equation defines a strongly monotone dynamical system. Our analyses of the other cases combine Lyapunov function arguments with a discrete choice theory result: that the choice probabilities generated by any additive random utility model can be derived from a deterministic model based on payoff perturbations that depend nonlinearly on the vector of choice probabilities.

This paper argues that incompleteness of intertemporal financial markets has little effect (on welfare, prices, or consumption) in an economy with a single consumption good, provided that traders are long–lived and patient, a riskless bond is traded, shocks are transitory, and there is no aggregate risk. In an economy with aggregate risk, a similar conclusion holds, provided traders share the same CRRA utility function and the right assets are traded. Examples demonstrate that these conclusions need not hold if the wrong assets are traded or if the economy has multiple consumption goods.

Backus, Kehoe, and Kydland (1992), Baxter and Crucini (1995), and Stockman and Tesar (1995) find two major discrepancies between standard international business cycle models with complete markets and the data: In the models, cross-country correlations are much higher for consumption than for output, while in the data the opposite is true; and cross-country correlations of employment and investment are negative, while in the data they are positive. This paper introduces a friction into a standard model that helps resolve these anomalies. The friction is that international loans are imperfectly enforceable; any country can renege on its debts and suffer the consequences for future borrowing. To solve for equilibrium in this economy with endogenous incomplete markets, the methods of Marcet and Marimon (1999) are extended. Incorporating the friction helps resolve the anomalies more than does exogenously restricting the assets that can be traded.

Stochastic dominance criteria are commonly used to draw welfare-theoretic inferences about comparisons of income distribution as well as ranking probability distributions in the analysis of choice under uncertainty. However, just as some measures of location and dispersion can be catastrophically sensitive to extreme values in the data it is also possible that conclusions drawn from empirical implementations of dominance criteria are unduly influenced by data contamination. We show the conditions under which this may occur for a number of standard dominance tools used in welfare analysis.

We develop a Ricardian trade model that incorporates realistic geographic features into general equilibrium. It delivers simple structural equations for bilateral trade with parameters relating to absolute advantage, to comparative advantage (promoting trade), and to geographic barriers (resisting it). We estimate the parameters with data on bilateral trade in manufactures, prices, and geography from 19 OECD countries in 1990. We use the model to explore various issues such as the gains from trade, the role of trade in spreading the benefits of new technology, and the effects of tariff reduction. Copyright The Econometric Society 2002.

An unresolved problem in Bayesian decision theory is how to value and price information. This paper resolves both problems assuming inexpensive information. Building on Large Deviation Theory, we produce a generically complete asymptotic order on samples of i.i.d. signals in finite–state, finite–action models. Computing the marginal value of an additional signal, we find it is eventually exponentially falling in quantity, and higher for lower quality signals. We provide a precise formula for the information demand, valid at low prices: asymptotically a constant times the log price, and falling in the signal quality for a given price.

This paper studies the relation between discrete–time and continuous–time principal–agent models. We derive the continuous–time model as a limit of discrete–time models with ever shorter periods and show that optimal incentive schemes in the discrete–time models approximate the optimal incentive scheme in the continuous model, which is linear in accounts. Under the additional assumption that the principal observes only cumulative total profits at the end and the agent can destroy profits unnoticed, an incentive scheme that is linear in total profits is shown to be approximately optimal in the discrete–time model when the length of the period is small.