Val E. Lambson

On the effects of entry in Cournot markets

In the framework of symmetric Cournot oligopoly, this paper provides two minimal sets of assumptions on the demand and cost functions that imply respectively that, as the number of firms increases, the minimal and maximal equilibria lead to (i) decreasing industry price and increasing or decreasing per-firm output; and (ii) increasing industry price (and decreasing per-firm output). In both cases, per-firm profits are decreasing. The analysis relies crucially on lattice-theoretic methods and yields general, unambiguous and easily interpretable conclusions of a global nature. As a byproduct of independent interest, new insight into existence of Cournot equilibrium is developed.

Industry evolution with sunk costs and uncertain market conditions

Firms often make decisions which entail sunk costs and have long-lasting effects. For example firms often must decide which technology to install in a plant without knowing what market conditions will prevail during the life of the plant. This paper presents a dynamic competitive equilibrium framework in which to analyze these issues.

Self-enforcing collusion in large dynamic markets

Abstract The “folk theorem” in game theory implies that any outcome that is better for all players than some single period Nash outcome can be achieved through noncooperative equilibrium in repeated games with discounting. Whether the folk theorem holds for a repeated Cournot oligopoly as the number of firms, N , increases without bound, is investigated. It is shown that the folk theorem holds in the limit iff demand increases at the same rate as the number of firms and the Cournot price sequence is bounded strictly above by the supremum of marginal cost for large N .

Competitive Profits in the Long Run

Profit rates differ across industries. Explanations have often relied on static models of imperfect competition. This paper develops a dynamic model of perfect competition to demonstrate that long-run average profit rates differ even across competitive industries when the effects of sunk costs on entry and exit are considered. The hypothesis that firms maximize their present expected values has few empirical implications for long-run average profit rates, but it does have implications for the behaviour of variables over time; for example, industries with high variability in the number of firms should exhibit low variability in firm values.

Entry, exit, and imperfect competition in the long run

An infinite-horizon, stochastic model of entry and exit with sunk costs and imperfect competition is constructed. Simple examples provide insights into: (1) the relationship between sunk costs and industry concentration, (2) entry when current profits are negative, and (3) the relationship between entry and the length of the product cycle. A subgame perfect Nash equilibrium for the general dynamic stochastic game is shown to exist as a limit of finite-horizon equilibria. This equilibrium has a relatively simple structure characterized by two numbers per finite history. Under very general conditions, it tends to exhibit excessive entry and insufficient exit relative to a social optimum.

The effects of sunk costs on entry and exit: evidence from 36 countries

Abstract Dynamic competitive models of industry evolution suggest that intertemporal variability of the number of firms should be lower in industries with higher sunk costs. We test this proposition using data from 36 countries. The results are consistent with the theory.

Sunk Costs and the Variability of Firm Value over Time

Empirical implications for the variability of firm value in various models of industry evolution are discussed. Under certain conditions, learning models imply that industries with higher sunk costs should exhibit greater difference in firm value between entering and exiting firms whereas external shocks models imply that industries with higher sunk costs should exhibit greater variability of firm value over time relative to a numeraire industry. The theoretical results from external shocks models are consistent with agricultural data from California and Florida. Copyright 1995 by MIT Press.

SUNK COSTS, PROFIT VARIABILITY, AND TURNOVER

Dynamic competitive models of industry evolution suggest that firm profit will be more volatile, and turnover lower, in industries with higher sunk costs. These implications are consistent with empirical observation. (JEL L00) Copyright 2006, Oxford University Press.

Dynamic Behaviour in Large Markets for Differentiated Products

An important question is how well competitive models approximate models of large finite economies. For a class of differentiated products models static Nash equilibria, if they exist, always converge to competition as the number of firms increases. Dynamic Nash equilibria need not so converge. Easily checked conditions for convergence to competition do, however, exist.

Learning by matching patterns

Abstract We analyze a model of repeated play between two boundedly rational agents. In each stage each player recalls the outcomes from the most recent few rounds, calculates the distribution of its opponents past reactions to this outcome pattern, and then optimizes myopically against this distribution. If both players use the same pattern length then the limit points of pattern matching are in the convex hull of the limit points of fictitious play. Thus if fictitious play converges into the set of Nash equilibria then pattern matching converges into the convex hull of Nash equilibria. If the players use different pattern lengths, the more sophisticated player may, but does not generally, succeed in playing as if it could perfectly predict its opponents play.