Economic Theory

The rate of convergence to Nash equilibrium of continuous fictitious play is determined for a generic set of utilities and initial beliefs in 2 × 2 games. In addition, an example is provided comparing the rate of convergence of discrete fictitious play to the rate for continuous fictitious play. Finally, the convergent dynamic of fictitious play is related to the nonconvergent gradient process dynamic in 2 × 2 games.

We propose a general model of oligopoly with firms relying on a two factor production function. In a first stage, firms choose a certain fixed factor level. In the second stage, firms compete on price and adjust the variable factor to satisfy all the demand. When the factors are substitutable, the capacity constraint is “soft,” implying a convex cost function in the second stage. We show that there exists a continuum of subgame perfect equilibria in pure strategies, whatever the returns to scale. Among them, a payoff dominant one can always be selected. The equilibrium price may increase with the number of firms.

This paper addresses the question of what one can learn about the dynamics of an economy from observing cross-sectional and time series variations in the volatility of prices in an arbitrage-free securities market. We introduce the notions of stochastic derivatives, marginal risk-adjusted growth rates, and marginal risk exposure in a single factor economy. We show that future variations in the state of the economy are due to two independent sources: the marginal risk-adjusted growth rate and the changes in marginal risk exposure. Using the martingale characterization of arbitrage-free prices, together with a martingale representation formula due to Haussmann (1978), we show that cross sectional variations in price volatility of assets with linear payoffs can be used to identify the sum of these two sources. Measurements of price volatility for assets with linear payoffs are not sufficient for complete identification of the independent determinants of possible future variations in the economy. However, using the volatility of prices of options on the state variable, we can identify the stochastic derivative and hence compute the price volatility of any path independent contingent claim.

Using a principal-agent setting, we introduce honesty that requires pre-commitment. The principal offers a menu of mechanisms to screen ethics. Agents may misrepresent ethics. Dishonest agents may misrepresent the match with the assigned task (good or bad), while honest agents reveal the match honestly if they have pre-committed. Ethics-screening, that allows for match-screening with dishonest agents while leaving a lower rent to honest agents, is optimal if both honesty and a good match are likely. Otherwise the optimal mechanism is the standard second-best or the first-best (where dishonest agents misrepresent the match), if dishonesty is likely or unlikely respectively.

The problem of revealed stochastic preference is whether probability distributions of observed choices in a population for various choice situations are consistent with a hypothesis of maximization of preference preorders by members of the population. This is a population analog of the classical revealed preference problem in economic consumer theory. This paper synthesizes the solutions to this problem that have been obtained by Marcel K. Richter and the author, and by J. C. Falmagne, in the case of finite sets of alternatives, and utilizes unpublished research of Richter and the author to give results for the non-finite choice sets encountered in economic consumer theory.

This paper considers the problem of a Principal who faces a privately informed Agent and only knows one moment of the type’s distribution. Preferences are nonlinear in the allocation, and the Principal maximizes her worst-case expected profits. The robustness property of the optimal mechanism imposes restrictions on the Principal’s ex-post payoff function: subject to the allocation being nonzero, ex-post payoffs are linear in the Agent’s type. The robust mechanism entails exclusion of low types, distortions at the intensive margin and efficiency at the top. We show that, under some conditions, distortions in the optimal mechanism are decreasing in types. This monotonicity has relevant consequences for several applications discussed. Our characterization uses an auxiliary zero-sum game played by the Principal and an adversarial Nature who seeks to minimize her expected payoffs which also gives us a characterization of the worst-case distribution from the Principal’s perspective. Applications of our framework to insurance provision, optimal taxation, nonlinear pricing and regulation are discussed.

Under take-it-or-leave-it offers, dynamic equilibria in the discrete time random matching model of money are a “translation” of dynamic equilibria in the standard overlapping generations model. This formalizes earlier conjectures about the equivalence of dynamic behavior in the two models and implies the indeterminacy of dynamic equilibria in the random matching model. As in the overlapping generations model, the indeterminacy disappears if an arbitrarily small utility to holding money is introduced. We introduce a different pricing mechanism, one that puts into sharp focus that agents are forward-looking when they interact.

We present a general revealed preference theorem concerning stochastic choice behavior by consumers. We show that, when the consumer spends her entire wealth, the Weak Axiom of Stochastic Revealed Preference due to Bandyopadhyay, Dasgupta, and Pattanaik (1999) is equivalent to a restriction on stochastic demand behavior that we call stochastic substitutability. We also show that the relationship between the Weak Axiom of Revealed Preference and Samuelson's inequality in the deterministic theory, and the main result of Bandyopadhyay, Dasgupta, and Pattanaik (1999) are both special cases of our result.