Rafael Rob

Learning, Mutation and Long Run Equilibria in Games

An evolutionary model with a finite number of players and with stochastic mutations is analyzed. The expansion and contraction of strategies is linked to their current relative success, but mutuation, perturbing the system from its deterministic evolution, are present as well. The focus is on the long run implications of ongoing mutations, which drastically reduce the set of equilibria. For 2 by 2 symmetric games with two symmetric strict Nash equilibria the risk dominant equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium. Copyright 1993 by The Econometric Society.

The Growth and Diffusion of Knowledge

This paper analyzes a decentralized process for the diffusion of knowledge. In equilibrium, the economy converges from an initial distribution of knowledge over agents to the steady-state distribution, which is unique. Because of the public good aspect of information, too little learning takes place, and ideas are implemented too early. The key difference between earlier formulations of search externalities by Diamond, Mortensen, and Spence on the one hand, and our own on the other, is that here spillovers of knowledge depend not only on how hard people are trying, but also on the differences in what they know: if all of us know the same thing, we cannot learn from each other. The model also addresses the following two substantive questions: first, the relationship between inequality and growth, noted some time ago by Kuznets, and second, the effect on growth of improvements in the communication technology.

Equilibrium Price Distributions

Equilibrium price distributions (for a homogeneous product) consistent with individual incentives are investigated. They arise in informationally imperfect markets in which the only primitive datum is the distribution of search costs. It is shown that single, multi- and continuous price distributions are all viable long-run phenomena depending on the nature of search costs. A method for computing equilibrium price distributions is also provided.

p-Dominance and belief potential

This paper elucidates on the logic behind recent papers which show that a unique equilibrium is selected in the presence of higher order uncertainty, i.e., when players lack common knowledge. We introduce two new concepts: stochastic potential of the information system and p-dominance of Nash-equilibria of the game, and show that a Nash-equilibrium is uniquely selected whenever its p-dominance is below the stochastic potential. This criterion applies to many-action games, not merely 2 by 2 games. It also applies to games without dominant strategies, where the set of equilibria is shown to be smaller and simpler than might be initially conjectured. Finally, the new concepts help understand the circumstances under which the set of equilibria varies with the amount of common knowledge among players. Copyright 1995 by The Econometric Society.

Learning and Capacity Expansion under Demand Uncertainty

A competitive, dynamic model of entry into a new industry is set up and both its positive and normative aspects are studied. The main assumptions are that entry is sequential, that it occurs under imperfect information on the size of the market and that better information becomes available as time goes on. The gradual improvement in information is due to the fact that later waves of entrants are able to observe the profitability of earlier entrants. The major results reported here (under suitable restrictions) are that the equilibrium rate of entry is monotonically decreasing over time, and that—at any given point in time—it is smaller than the socially optimal one.

Pollution claim settlements under private information

Abstract The classical problem of resolving a nuisance dispute between a pollution-generating firm and nearby residents is modelled here as a mechanism-design problem. We assume that the designer of the mechanism is the firm, that it is uncertain about the actual losses suffered by residents and that the initial assignment of property rights is one where each resident is entitled to prevail. We derive a profitmaximizing scheme under the individual-rationality and incentive-compatibility constraints and examine its properties. It is shown that the outcomes it yields are sometimes inefficient. Moreover, when many residents are affected by pollution and the degree of uncertainty with respect to the losses they suffer is large, these inefficiencies become rampant.

Long Waves and Short Waves: Growth Through Intensive and Extensive Search

This paper endogenizes the frequency of major discoveries and the extent of their refinement. Four axioms deliver a one-parameter family of beliefs that guide exploratory effort. Such effort trades off the prospect of major new discovery against the chance of successfully refining discoveries made in the past. The only other parameter is the cost of making new discoveries relative to the cost of refining old ones. The paper derives time-series properties of inventive activity as they relate to the two parameters, and it discusses several specific inventions and their subsequent refinement. Copyright 1990 by The Econometric Society.

Piracy on the Silver Screen

New information technology has reduced marginal production and distribution costs of information goods to negligible levels and promises to revolutionize many industries. Unpaid copies of digital products can be as good as paid first-generation copies, and their availability can undermine the ability of sellers to cover first-copy costs. As a result, unpaid distribution has emerged as a major issue facing the music and movie industries in the past few years. Using survey data on movie consumption by about 500 University of Pennsylvania college students, we ask whether unpaid consumption of movies displaces paid consumption. Employing a variety of cross-sectional and longitudinal empirical approaches, we find large and statistically significant evidence of displacement. In what we view as the most appropriate empirical specifications, we find that unpaid first consumption reduces paid consumption by about 1 unit. Unpaid second consumption has a smaller effect, about 0.20 units. These estimates indicate that unpaid consumption, which makes up 5.2 percent of movie viewing in our sample, reduced paid consumption in our sample by 3.5 percent.

Product Innovation by a Durable-Good Monpoly

We consider a durable-good monopolist that periodically introduces new models, each new model representing an improvement upon its predecessor. We show that if the monopolist is able neither to exercise planned obsolescence (i.e., artificially shorten the lift of its products) nor to give discounts to repeat customers, the rate of product introductions is too slow -- in comparison with the social optimum. On the other hand, if the monopolist is able to artificially shorten the durability of its products or to offer price discounts to repeat customers, it can raise its profit and, at the same time, implement the social optimum.

Is Bigger Better? Customer Base Expansion through Word‐of‐Mouth Reputation

A model of gradual reputation formation through a process of continuous investment in product quality is developed. We assume that the ability to produce high‐quality products requires continuous investment and that as a consequence of informational frictions, such as search costs, information about firms’ past performance diffuses only gradually in the market. This leads to a dual process of growth of a firm’s customer base and an increase in the firm’s investment in quality. The model predicts, therefore, that the longer its tenure as a high‐quality producer, the more a firm invests in quality. We relate this finding to empirical work on online commerce as well as on traditional industries.