Theories of imperfectly competitive markets
type: Item
instance of: scholarly article
title: Theories of imperfectly competitive markets
zbMATH Open document ID: 0911.90044
published in: Lecture Notes in Economics and Mathematical Systems
publication date: 1996-11-14T00:00:00Z
review text: The author provides a systematic treatment of some models of imperfect competition relying on published works in the area, including the author's own. The opening chapter on non-cooperative game theory devotes a section on aggregative games, where the sum of the strategies of the other players is the relevant variable in each payoff function, aside from the player's own strategy. Under some regularity conditions, the most prominent of which is a condition that the inverse demand function be concave or ``not too convex'', existence of a unique and stable Nash equilibrium is established. Stability is considered in the context of two types of dynamic models, one in which agents change their strategies in the direction of the best reply strategies (best reply dynamics) and another in which agents increase their strategy if and only if the marginal payoff is positive (gradient dynamics). Aggregative games are not suitable for games of price setting behaviour where strategies of competitors enter separately in payoffs. A separate section is devoted to a similar analysis of this type of games under dominant diagonal type assumptions ensuring stability. A chapter on comparative statics investigates, in the context of both the quantity setting Cournot model as well as the price setting Bertrand model, the effects of changes in the number of players, and in the payoff functions, on the Nash equilibrium strategies and payoffs. Various propositions are established, for example, that the effect of a new entrant is to increase aggregate output and decrease the output and payoffs of the incumbents. Effect of shifts in the payoff functions, both for individual players as well as generalized shifts for all players, are analyzed. It is shown that effects of changes in marginal costs on price is not unambiguously more for imperfectly competitive markets than for competitive ones, but rather depends on the degree of concavity of the inverse demand function. Welfare properties of market…
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 91A40
Mathematics Subject Classification ID: 91-02
Mathematics Subject Classification ID: 91A80
Mathematics Subject Classification ID: 91A10
zbMATH DE Number: 945669
zbMATH Keywords: best reply dynamics
zbMATH Keywords: gradient dynamics
zbMATH Keywords: aggregative games
zbMATH Keywords: quantity setting Cournot model
zbMATH Keywords: price setting Bertrand model
zbMATH Keywords: market allocations
zbMATH Keywords: incomplete information
zbMATH Keywords: subgame perfect Nash equilibrium
author: Luis Corchón
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 945669