The Theory of Oligopoly with Multi-Product Firms

In the mid 1960's both authors undertook independent works in oligopoly.and game theory. However, it was not until 1983 that they formally met. Since then, they have continued meeting either in Budapest or Tokyo. Their collaboration has resulted in numerous publications as well as in this work. Essentially, this book has two origins. First, it originated in previous results, either published or circulated in mimeograph form. Finely sifting their results, the authors constructed a concise reinterpretation of their achievement to date. However, this unifying process led to the second origin. Reconsideration, particularly in this comprehensive approach, generated new results. This was especially true in the analysis of the existence, uniqueness and global stability of the Cournot-Nash equilibrium for oligopoly with multi-product flrms, and for several modilled Cournot and related models. This book should be ideal for graduate students in economics or mathematics. However, as the authors have firmly grounded their ideas in the formal language of mathematics, the student should possess some background in calculus, linear algebra, and ordinary differential and difference equations. Additionally, the book should be useful to researchers in oligopoly and game theory as well as to mathematically oriented economists. The methodology developed for analyzing the existence and stability of oligopoly equilibrium should prove useful also in theoretical analysis of other economic models. Weare both very grateful to Professor Wilhelm Krelle for his careful review and helpful suggestions. In addition, Koji Okuguchi wishes to thank Professors W.

Examination of the existence, uniqueness, and stability of Cournot-Nash equilibrium of multi-product oligopolies Extension of the results to several model variants and generalizations Constructive existence proofs and general methodology to establish stability Comprehensive review of the field and future research directions

Klappentext

This book gives a comprehensive survey and complete mathematical development of the theory of multi-product oligopolies. Existence and uniqueness of the Nash-Cournot equilibria as well as its stability are analysed for the multi-product Cournot model and for its variants such as labor-managed industries, saturated markets, rent-seeking oligopolies and presence of production adjustment costs. Applications are discussed for network oligopolies, taxation, water resources management, and international fishery. The controllability of multi-product Cournot markets is also briefly analysed.

Inhalt
1 Introduction.- 2 Oligopoly Games and Their Extensions.- 2.1 The Cournot Model.- 2.2 Models with Product Differentiation.- 2.3 Multiproduct Models.- 2.4 Group Equilibrium Problems.- 2.5 Rent Seeking Models.- 2.6 Labor-Managed Oligopoly.- 2.7 Oligopsony.- 2.8 Two-Stage and Multi-Stage Oligopolies.- 2.9 A Hierarchical Model.- 2.10 Supplementary Notes and Discussions.- 3 Existence and Uniqueness Results.- 3.1 Existence Results for Multiproduct Oligopoly.- 3.2 Relation of Equilibrium Problems to Fixed Point and Nonlinear Complementarity Problems.- 3.3 Uniqueness and Properties of Equilibria in the Classical Game.- 3.4 Linear Oligopoly Models.- 3.5 Numerical Methods for Finding Cournot-Nash Equilibria.- 3.6 Existence of Equilibrium in Rent Seeking Games.- 3.7 Existence of Equilibrium in Labor-Managed Oligopolies.- 3.8 Existence of Equilibrium in Oligopsony.- 3.9 Supplementary Notes and Discussions.- 4 Dynamic Oligopoly with Discrete Time Scale.- 4.1 Cournot Expectations.- 4.2 Adaptive Expectations.- 4.3 Sequential Adjustment Processes.- 4.4 Extrapolative Expectations.- 4.5 Oligopoly with Market Saturation.- 4.6 Quasioptimal Output Selections.- 4.7 Production Adjustment Costs.- 4.8 Dynamic Rent Seeking Oligopolies.- 4.9 Dynamic Labor-Managed Oligopolies.- 4.10 Dynamic Oligopsonies.- 4.11 Supplementary Notes and Discussions.- 5 Dynamic Oligopoly with Continuous Time Scale.- 5.1 Classical Results.- 5.2 Adaptive Expectations.- 5.3 Extrapolative Expectations.- 5.4 Oligopoly with Market Saturation.- 5.5 Production Adjustment Costs.- 5.6 Dynamic Rent Seeking Oligopolies.- 5.7 Dynamic Labor-Managed Oligopolies.- 5.8 Dynamic Oligopsonies.- 5.9 Supplementary Notes and Discussions.- 6 Extensions and Generalizations.- 6.1 Quadratic Games Under Discrete Time Scale.- 6.2 Quadratic GamesUnder Continuous Time Scale.- 6.3 Nonlinear Oligopolies Under Discrete Time Scale.- 6.4 Nonlinear Oligopolies Under Continuous Time Scale.- 6.5 Supplementary Notes and Discussions.- 7 Applications.- 7.1 Network Oligopolies.- 7.2 Taxation.- 7.3 Water Resources Applications.- 7.4 An Oligopoly Model of Commercial Fishing.- 7.5 Controllability in Oligopolies.- 7.6 Supplementary Notes and Discussions.- References.