This paper develops a model of strategic communication, in which a better-informed Sender (S) sends a possibly noisy signal to a Receiver (R), who then takes an action that determines the welfare of both. We characterize the set of Bayesian Nash equilibria under standard assumptions, and show that equilibrium signaling always takes a strikingly simple form, in which S partitions the support of the (scalar) variable that represents his private information and introduces noise into his signal by reporting, in effect, only which element of the partition his observation actually lies in. We show under further assumptions that before S observes his private information, the equilibrium whose partition has the greatest number of elements is Pareto-superior to all other equilibria, and that if agents coordinate on this equilibrium, R's equilibrium expected utility rises when agents' preferences become more similar. Since R bases his choice of action on rational expectations, this establishes a sense in which equilibrium signaling is more informative when agents' preferences are more similar.

Strategic Information Transmission

Strategic information transmission

The Theory of Monopolistic Competition.

A substantial portion of the increase in the output of advanced industrial nations is widely judged to have been attributable to technical progress. There is also overwhelming evidence that this progress has not occurred merely in a random manner (see, e.g. Schmookler, 1962}. Yet there is not much in the way of economic theory to explain either its rate or its direction, and particularly little that has a reasonably precise micro-economic foundation.^ This lacuna is important, because a recognition of the importance of technical progress raises serious doubts about the adequacy with which traditional micro-economic models allow one to understand the functioning of modern market economies, and to develop policy prescriptions (e.g. with respect to anti-trust policy). The lacuna is also surprising, for it has become a commonplace, at least since the work of Schumpetcr (1947), that the pace of inventive and innovative activity is related to market structure. Moreover, there must be many who share the Schumpeterian belief that perfect competition is inimical to inventive activity, and that the gains from such activity more than offset the welfare loss arising from production inefficiency associated with market power.^ However, a substantial part of the recent industrial organisation literature would appear to have interpreted tests of the Schumpeterian thesis in a somewhat different manner.^ It is often argued now that industrial concentration and large size spur inventive activity. It is as though concentration is a cause of innovations.^

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Industrial Structure and the Nature of Innovative Activity

International trade in the presence of product differentiation, economies of scale and monopolistic competition: A Chamberlin-Heckscher-Ohlin approach

This paper examines the existence of n-firm Cournot equilibrium in a market for a single homogeneous commodity. It proves that if each firm's marginal revenue declines as the aggregate output of other firms increases (which is implied by concave inverse demand) then a Cournot equilibrium exists, without assuming that firms have nondecreasing marginal cost or identical technologies. Also, if the marginal revenue condition fails at a "potential optimal point," there is a set of firms such that no Cournot equilibrium exists. The paper also contains an example of nonexistence with two nonidentical firms, each with constant returns to scale production.

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On the Existence of Cournot Equilibrium

This article studies the fulfilled expectations equilibrium for a Cournot duopoly model in which firms acquire information about uncertain linear demand Several propositions are established concerning the incentives to acquire and release information in this duopoly environment

Fulfilled Expectations Cournot Duopoly with Information Acquisition and Release

Despite the fact that the assumptions underlying perfect competition never actually hold, the use of the competitive model, as an idealization, is justified if the predictions of the model approximate the outcomes of situations it is used to represent. In partial equilibrium analysis, this justification is embodied in the " Folk Theorem " which states that if firms are small relative to the market, then the market outcome is approximately competitive. This paper provides a precise statement and proof of the " Folk Theorem " for competitive markets with a single homogeneous good, and free entry and exit. It is shown that if firms are small relative to the market then there is a Cournot equilibrium with free entry; furthermore, any Cournot equilibrium with free entry is approximately competitive. More specifically, if we consider an appropriate sequence of markets in which firms become arbitrarily small relative to the market, then there is a Cournot equilibrium with free entry for all markets in the tail of the sequence, and aggregate equilibrium output converges to perfectly competitive output. If firms have strictly U-shaped average cost curves, then individual firm behaviour converges to competitive behaviour. The treatment of free entry distinguishes this paper from other papers dealing with the " Folk Theorem ", where either the number of firms is exogeneous, ruling out free entry, or free entry is treated as being equivalent to a zero profit condition, ignoring the integer problem that arises when the number of firms is finite but unspecified. Firms may become small relative to the market in two ways: through changes in technology, absolute firm size (the smallest output at which minimum average cost is attained) may become small, or, through shifts in demand, the absolute size of the market (the market demand at competitive price) may become large. We allow both types of changes here, though shifts in demand, especially in the form of replication of the consumer sector, may be more familiar. In his conclusion, Ruffin (1971) presents a verbal argument for the " Folk Theorem " which is based on replication of demand and entry. Hart (1979), though not concerned with existence, shows that in a general equilibrium model with differentiated products and free entry, equilibria are approximately competitive (Pareto optimal) when consumers have been replicated a sufficient number of times. The paper is organized as follows: Section 1 contains the perfectly competitive model and its assumptions, Section 2 contains the assumptions and definitions for the imperfectly competitive model, Section 3 contains an example contrasting the usual treatment of the " Folk Theorem" and the present approach, Section 4 contains the proofs of the main results, and Section 5 contains remarks on the results and indicates how some of the assumptions that are used can be weakened.

Cournot Equilibrium with Free Entry

Equilibrium in simple spatial (or differentiated product) models

The purpose of this essay is to explain a new theory of perfect competition that synthesizes the Arrow-Debreu-McKenzie and Marshallian theories and summarizes the recent work of a large number of researchers. The synthetic theory provides a logically precise general equilibrium framework that can be used both for positive analysis as well as to form a basis for the classical theorems of welfare economics; in these aspects it follows the ADM theory. However, as in the Marshallian theory, there is free-entry in the form of an unbounded pool of firms which have access to the existing technology. Also as in the Marshallian theory, the average cost curves available to each firm are U-shaped.
In contrast to both the Marshallian and the ADM theories, we do not take price taking as a hypothesis. We use the term "perfect competition" to describe a situation in which firms are arbitrarily small relative to the markets in which they are involved. The firms in our model correctly perceive the effect of the amount that they place on the market on prices and they act to maximize profit with this in mind. "Perfectly competitive equilibria" are defined as the limit points of equilibria as firms become small relative to the market, and following Cournot, we observe that as firms become small their ability to influence price disappears.
A new condition is identified which is important for the viability of competitive markets. Loosely speaking, this condition requires that prices provide the proper entry signals for firms. If one thinks of each firm as associated with the use of an unpriced and nondivisible resource, sometimes referred to as entrepreneurship, then in equilibrium the returns to that factor must fall with entry and rise with exit. Not only the stability theorems of the synthetic theory but also the existence theorem reject the application of the competitive model to a regime in which entry drives up (and exit reduces} the profit of similar firms.

William Novshek

Papers

On the Existence of Cournot Equilibrium

Fulfilled Expectations Cournot Duopoly with Information Acquisition and Release

Cournot Equilibrium with Free Entry

Equilibrium in simple spatial (or differentiated product) models

General Equilibrium with Free Entry: A Synthetic Approach to the Theory of Perfect Competition*